x^2-46x=-6x^2-24

Solution for x^2-46x=-6x^2-24 equation:

x^2-46x=-6x^2-24

We move all terms to the left:

x^2-46x-(-6x^2-24)=0

We get rid of parentheses

x^2+6x^2-46x+24=0

We add all the numbers together, and all the variables

7x^2-46x+24=0

a = 7; b = -46; c = +24;
Δ = b2-4ac
Δ = -462-4·7·24
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-38}{2*7}=\frac{8}{14}
=4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+38}{2*7}=\frac{84}{14}
=6
$