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x=4x^2-12x-15
We move all terms to the left:
x-(4x^2-12x-15)=0
We get rid of parentheses
-4x^2+x+12x+15=0
We add all the numbers together, and all the variables
-4x^2+13x+15=0
a = -4; b = 13; c = +15;
Δ = b2-4ac
Δ = 132-4·(-4)·15
Δ = 409
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{409}}{2*-4}=\frac{-13-\sqrt{409}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{409}}{2*-4}=\frac{-13+\sqrt{409}}{-8} $
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