12x^2-15x-3=3

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

12x^2-15x-3=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

12x^2-15x-6=0

a = 12; b = -15; c = -6;
Δ = b2-4ac
Δ = -152-4·12·(-6)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{57}}{2*12}=\frac{15-3\sqrt{57}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{57}}{2*12}=\frac{15+3\sqrt{57}}{24}
$