12x^2+30x-8=0

Solution for 12x^2+30x-8=0 equation:

12x^2+30x-8=0

a = 12; b = 30; c = -8;
Δ = b2-4ac
Δ = 302-4·12·(-8)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{321}}{2*12}=\frac{-30-2\sqrt{321}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{321}}{2*12}=\frac{-30+2\sqrt{321}}{24}
$