8x^2-5x=13

Solution for 8x^2-5x=13 equation:

8x^2-5x=13

We move all terms to the left:

8x^2-5x-(13)=0

a = 8; b = -5; c = -13;
Δ = b2-4ac
Δ = -52-4·8·(-13)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-21}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+21}{2*8}=\frac{26}{16}
=1+5/8
$