X^2-2x-10=7x+12

Solution for X^2-2x-10=7x+12 equation:

X^2-2X-10=7X+12

We move all terms to the left:

X^2-2X-10-(7X+12)=0

We get rid of parentheses

X^2-2X-7X-12-10=0

We add all the numbers together, and all the variables

X^2-9X-22=0

a = 1; b = -9; c = -22;
Δ = b2-4ac
Δ = -92-4·1·(-22)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-13}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+13}{2*1}=\frac{22}{2}
=11
$