8b^2-10b=13

Solution for 8b^2-10b=13 equation:

8b^2-10b=13

We move all terms to the left:

8b^2-10b-(13)=0

a = 8; b = -10; c = -13;
Δ = b2-4ac
Δ = -102-4·8·(-13)
Δ = 516
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{129}}{2*8}=\frac{10-2\sqrt{129}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{129}}{2*8}=\frac{10+2\sqrt{129}}{16}
$