4x^2-46x-126=0

Solution for 4x^2-46x-126=0 equation:

4x^2-46x-126=0

a = 4; b = -46; c = -126;
Δ = b2-4ac
Δ = -462-4·4·(-126)
Δ = 4132
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:

$\sqrt{\Delta}=\sqrt{4132}=\sqrt{4*1033}=\sqrt{4}*\sqrt{1033}=2\sqrt{1033}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{1033}}{2*4}=\frac{46-2\sqrt{1033}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{1033}}{2*4}=\frac{46+2\sqrt{1033}}{8}
$