x^2+45x-17=12x+2

Solution for x^2+45x-17=12x+2 equation:

x^2+45x-17=12x+2

We move all terms to the left:

x^2+45x-17-(12x+2)=0

We get rid of parentheses

x^2+45x-12x-2-17=0

We add all the numbers together, and all the variables

x^2+33x-19=0

a = 1; b = 33; c = -19;
Δ = b2-4ac
Δ = 332-4·1·(-19)
Δ = 1165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{1165}}{2*1}=\frac{-33-\sqrt{1165}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1165}}{2*1}=\frac{-33+\sqrt{1165}}{2}
$