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96=45x^2
We move all terms to the left:
96-(45x^2)=0
a = -45; b = 0; c = +96;
Δ = b2-4ac
Δ = 02-4·(-45)·96
Δ = 17280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17280}=\sqrt{576*30}=\sqrt{576}*\sqrt{30}=24\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{30}}{2*-45}=\frac{0-24\sqrt{30}}{-90} =-\frac{24\sqrt{30}}{-90} =-\frac{4\sqrt{30}}{-15} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{30}}{2*-45}=\frac{0+24\sqrt{30}}{-90} =\frac{24\sqrt{30}}{-90} =\frac{4\sqrt{30}}{-15} $
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