2x-3+12+2x-3+x^2+2x=78

Solution for 2x-3+12+2x-3+x^2+2x=78 equation:

2x-3+12+2x-3+x^2+2x=78

We move all terms to the left:

2x-3+12+2x-3+x^2+2x-(78)=0

We add all the numbers together, and all the variables

x^2+6x-72=0

a = 1; b = 6; c = -72;
Δ = b2-4ac
Δ = 62-4·1·(-72)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*1}=\frac{12}{2}
=6
$