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4(-4x^2)+2x+5=-57
We move all terms to the left:
4(-4x^2)+2x+5-(-57)=0
We add all the numbers together, and all the variables
4(-4x^2)+2x+62=0
We multiply parentheses
-16x^2+2x+62=0
a = -16; b = 2; c = +62;
Δ = b2-4ac
Δ = 22-4·(-16)·62
Δ = 3972
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3972}=\sqrt{4*993}=\sqrt{4}*\sqrt{993}=2\sqrt{993}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{993}}{2*-16}=\frac{-2-2\sqrt{993}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{993}}{2*-16}=\frac{-2+2\sqrt{993}}{-32} $
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