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9^2+4x+7=3x^2-8
We move all terms to the left:
9^2+4x+7-(3x^2-8)=0
We add all the numbers together, and all the variables
4x-(3x^2-8)+88=0
We get rid of parentheses
-3x^2+4x+8+88=0
We add all the numbers together, and all the variables
-3x^2+4x+96=0
a = -3; b = 4; c = +96;
Δ = b2-4ac
Δ = 42-4·(-3)·96
Δ = 1168
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{73}}{2*-3}=\frac{-4-4\sqrt{73}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{73}}{2*-3}=\frac{-4+4\sqrt{73}}{-6} $
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