4b^2=-3b+45

Solution for 4b^2=-3b+45 equation:

4b^2=-3b+45

We move all terms to the left:

4b^2-(-3b+45)=0

We get rid of parentheses

4b^2+3b-45=0

a = 4; b = 3; c = -45;
Δ = b2-4ac
Δ = 32-4·4·(-45)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*4}=\frac{-30}{8}
=-3+3/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*4}=\frac{24}{8}
=3
$