12x^2+15x-2=-5

Solution for 12x^2+15x-2=-5 equation:

12x^2+15x-2=-5

We move all terms to the left:

12x^2+15x-2-(-5)=0

We add all the numbers together, and all the variables

12x^2+15x+3=0

a = 12; b = 15; c = +3;
Δ = b2-4ac
Δ = 152-4·12·3
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*12}=\frac{-24}{24}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*12}=\frac{-6}{24}
=-1/4
$