4x^2-16x=113

Solution for 4x^2-16x=113 equation:

4x^2-16x=113

We move all terms to the left:

4x^2-16x-(113)=0

a = 4; b = -16; c = -113;
Δ = b2-4ac
Δ = -162-4·4·(-113)
Δ = 2064
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:

$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{129}}{2*4}=\frac{16-4\sqrt{129}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{129}}{2*4}=\frac{16+4\sqrt{129}}{8}
$