-4x^2+126x-574=0

Solution for -4x^2+126x-574=0 equation:

-4x^2+126x-574=0

a = -4; b = 126; c = -574;
Δ = b2-4ac
Δ = 1262-4·(-4)·(-574)
Δ = 6692
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:

$\sqrt{\Delta}=\sqrt{6692}=\sqrt{4*1673}=\sqrt{4}*\sqrt{1673}=2\sqrt{1673}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-2\sqrt{1673}}{2*-4}=\frac{-126-2\sqrt{1673}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+2\sqrt{1673}}{2*-4}=\frac{-126+2\sqrt{1673}}{-8}
$