12u2+52u=48

Solution for 12u2+52u=48 equation:

12u^2+52u=48

We move all terms to the left:

12u^2+52u-(48)=0

a = 12; b = 52; c = -48;
Δ = b2-4ac
Δ = 522-4·12·(-48)
Δ = 5008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5008}=\sqrt{16*313}=\sqrt{16}*\sqrt{313}=4\sqrt{313}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{313}}{2*12}=\frac{-52-4\sqrt{313}}{24}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{313}}{2*12}=\frac{-52+4\sqrt{313}}{24}
$