X2-12=4x-7

Solution for X2-12=4x-7 equation:

X2-12=4X-7

We move all terms to the left:

X2-12-(4X-7)=0

We add all the numbers together, and all the variables

X^2-(4X-7)-12=0

We get rid of parentheses

X^2-4X+7-12=0

We add all the numbers together, and all the variables

X^2-4X-5=0

a = 1; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·1·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*1}=\frac{10}{2}
=5
$