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-12x=3x^2+7
We move all terms to the left:
-12x-(3x^2+7)=0
We get rid of parentheses
-3x^2-12x-7=0
a = -3; b = -12; c = -7;
Δ = b2-4ac
Δ = -122-4·(-3)·(-7)
Δ = 60
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{15}}{2*-3}=\frac{12-2\sqrt{15}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{15}}{2*-3}=\frac{12+2\sqrt{15}}{-6} $
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