4b^2-7b=15

Solution for 4b^2-7b=15 equation:

4b^2-7b=15

We move all terms to the left:

4b^2-7b-(15)=0

a = 4; b = -7; c = -15;
Δ = b2-4ac
Δ = -72-4·4·(-15)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*4}=\frac{-10}{8}
=-1+1/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*4}=\frac{24}{8}
=3
$