4x^2-128x+100=0

Solution for 4x^2-128x+100=0 equation:

4x^2-128x+100=0

a = 4; b = -128; c = +100;
Δ = b2-4ac
Δ = -1282-4·4·100
Δ = 14784
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:

$\sqrt{\Delta}=\sqrt{14784}=\sqrt{64*231}=\sqrt{64}*\sqrt{231}=8\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-8\sqrt{231}}{2*4}=\frac{128-8\sqrt{231}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+8\sqrt{231}}{2*4}=\frac{128+8\sqrt{231}}{8}
$