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-12x=7x^2+5
We move all terms to the left:
-12x-(7x^2+5)=0
We get rid of parentheses
-7x^2-12x-5=0
a = -7; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·(-7)·(-5)
Δ = 4
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*-7}=\frac{10}{-14} =-5/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*-7}=\frac{14}{-14} =-1 $
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