12r^2+75r+108=0

Solution for 12r^2+75r+108=0 equation:

12r^2+75r+108=0

a = 12; b = 75; c = +108;
Δ = b2-4ac
Δ = 752-4·12·108
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-21}{2*12}=\frac{-96}{24}
=-4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+21}{2*12}=\frac{-54}{24}
=-2+1/4
$