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x=4x^2+12x-5
We move all terms to the left:
x-(4x^2+12x-5)=0
We get rid of parentheses
-4x^2+x-12x+5=0
We add all the numbers together, and all the variables
-4x^2-11x+5=0
a = -4; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·(-4)·5
Δ = 201
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{-(-11)-\sqrt{201}}{2*-4}=\frac{11-\sqrt{201}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{201}}{2*-4}=\frac{11+\sqrt{201}}{-8} $
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