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-12=-5(x^2)-10x
We move all terms to the left:
-12-(-5(x^2)-10x)=0
We get rid of parentheses
5x^2+10x-12=0
a = 5; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·5·(-12)
Δ = 340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{85}}{2*5}=\frac{-10-2\sqrt{85}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{85}}{2*5}=\frac{-10+2\sqrt{85}}{10} $
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