x=-4x^2+46x-126

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

x=-4x^2+46x-126

We move all terms to the left:

x-(-4x^2+46x-126)=0

We get rid of parentheses

4x^2-46x+x+126=0

We add all the numbers together, and all the variables

4x^2-45x+126=0

a = 4; b = -45; c = +126;
Δ = b2-4ac
Δ = -452-4·4·126
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3}{2*4}=\frac{42}{8}
=5+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3}{2*4}=\frac{48}{8}
=6
$