-3=-x^2-5x+12

Solution for -3=-x^2-5x+12 equation:

-3=-x^2-5x+12

We move all terms to the left:

-3-(-x^2-5x+12)=0

We get rid of parentheses

x^2+5x-12-3=0

We add all the numbers together, and all the variables

x^2+5x-15=0

a = 1; b = 5; c = -15;
Δ = b2-4ac
Δ = 52-4·1·(-15)
Δ = 85
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{-(5)-\sqrt{85}}{2*1}=\frac{-5-\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{85}}{2*1}=\frac{-5+\sqrt{85}}{2}
$