2x^2-100=46x

Solution for 2x^2-100=46x equation:

2x^2-100=46x

We move all terms to the left:

2x^2-100-(46x)=0

a = 2; b = -46; c = -100;
Δ = b2-4ac
Δ = -462-4·2·(-100)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-54}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+54}{2*2}=\frac{100}{4}
=25
$