16x^2-20x=13

Solution for 16x^2-20x=13 equation:

16x^2-20x=13

We move all terms to the left:

16x^2-20x-(13)=0

a = 16; b = -20; c = -13;
Δ = b2-4ac
Δ = -202-4·16·(-13)
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{77}}{2*16}=\frac{20-4\sqrt{77}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{77}}{2*16}=\frac{20+4\sqrt{77}}{32}
$