45=2x^2+7x-12

Solution for 45=2x^2+7x-12 equation:

45=2x^2+7x-12

We move all terms to the left:

45-(2x^2+7x-12)=0

We get rid of parentheses

-2x^2-7x+12+45=0

We add all the numbers together, and all the variables

-2x^2-7x+57=0

a = -2; b = -7; c = +57;
Δ = b2-4ac
Δ = -72-4·(-2)·57
Δ = 505
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{-(-7)-\sqrt{505}}{2*-2}=\frac{7-\sqrt{505}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{505}}{2*-2}=\frac{7+\sqrt{505}}{-4}
$