3u^2-5u-12=0

Solution for 3u^2-5u-12=0 equation:

3u^2-5u-12=0

a = 3; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·3·(-12)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*3}=\frac{-8}{6}
=-1+1/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*3}=\frac{18}{6}
=3
$