7x^2-12=3x+15

Solution for 7x^2-12=3x+15 equation:

7x^2-12=3x+15

We move all terms to the left:

7x^2-12-(3x+15)=0

We get rid of parentheses

7x^2-3x-15-12=0

We add all the numbers together, and all the variables

7x^2-3x-27=0

a = 7; b = -3; c = -27;
Δ = b2-4ac
Δ = -32-4·7·(-27)
Δ = 765
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{85}}{2*7}=\frac{3-3\sqrt{85}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{85}}{2*7}=\frac{3+3\sqrt{85}}{14}
$