4b^2-3b=8

Solution for 4b^2-3b=8 equation:

4b^2-3b=8

We move all terms to the left:

4b^2-3b-(8)=0

a = 4; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·4·(-8)
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{137}}{2*4}=\frac{3-\sqrt{137}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{137}}{2*4}=\frac{3+\sqrt{137}}{8}
$