5b^2=-12b+9

Solution for 5b^2=-12b+9 equation:

5b^2=-12b+9

We move all terms to the left:

5b^2-(-12b+9)=0

We get rid of parentheses

5b^2+12b-9=0

a = 5; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·5·(-9)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*5}=\frac{-30}{10}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*5}=\frac{6}{10}
=3/5
$