39x^2-52x-48=0

Solution for 39x^2-52x-48=0 equation:

39x^2-52x-48=0

a = 39; b = -52; c = -48;
Δ = b2-4ac
Δ = -522-4·39·(-48)
Δ = 10192
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:

$\sqrt{\Delta}=\sqrt{10192}=\sqrt{784*13}=\sqrt{784}*\sqrt{13}=28\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-28\sqrt{13}}{2*39}=\frac{52-28\sqrt{13}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+28\sqrt{13}}{2*39}=\frac{52+28\sqrt{13}}{78}
$