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Formula
Number of solution
$$4 x ^ { 2 } - 9 = 0$$
 2 real roots 
Find the number of solutions
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 9 } = \color{#FF6800}{ 0 }$
 Determine the number of roots using discriminant, $D=b^{2}-4ac$ from quadratic equation, $ax^{2}+bx+c=0$
$\color{#FF6800}{ D } = \color{#FF6800}{ 0 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 9 } \right )$
$D = \color{#FF6800}{ 0 } ^ { \color{#FF6800}{ 2 } } - 4 \times 4 \times \left ( - 9 \right )$
 The power of 0 is 0 
$D = \color{#FF6800}{ 0 } - 4 \times 4 \times \left ( - 9 \right )$
$D = \color{#FF6800}{ 0 } - 4 \times 4 \times \left ( - 9 \right )$
 0 does not change when you add or subtract 
$D = - 4 \times 4 \times \left ( - 9 \right )$
$D = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 9 } \right )$
 Multiply the numbers 
$D = \color{#FF6800}{ 144 }$
$\color{#FF6800}{ D } = \color{#FF6800}{ 144 }$
 Since $D>0$ , the number of real root of the following quadratic equation is 2 
 2 real roots 
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