-.75x^2+5x=-12

Solution for -.75x^2+5x=-12 equation:

-.75x^2+5x=-12

We move all terms to the left:

-.75x^2+5x-(-12)=0

We add all the numbers together, and all the variables

-0.75x^2+5x+12=0

a = -0.75; b = 5; c = +12;
Δ = b2-4ac
Δ = 52-4·(-0.75)·12
Δ = 61
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{61}}{2*-0.75}=\frac{-5-\sqrt{61}}{-1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{61}}{2*-0.75}=\frac{-5+\sqrt{61}}{-1.5}
$