-12x^2-15x+21=0

Solution for -12x^2-15x+21=0 equation:

-12x^2-15x+21=0

a = -12; b = -15; c = +21;
Δ = b2-4ac
Δ = -152-4·(-12)·21
Δ = 1233
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:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{137}}{2*-12}=\frac{15-3\sqrt{137}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{137}}{2*-12}=\frac{15+3\sqrt{137}}{-24}
$