5x^2-13x=16

Solution for 5x^2-13x=16 equation:

5x^2-13x=16

We move all terms to the left:

5x^2-13x-(16)=0

a = 5; b = -13; c = -16;
Δ = b2-4ac
Δ = -132-4·5·(-16)
Δ = 489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{489}}{2*5}=\frac{13-\sqrt{489}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{489}}{2*5}=\frac{13+\sqrt{489}}{10}
$