12-b(5b-9)=4b+3

Solution for 12-b(5b-9)=4b+3 equation:

12-b(5b-9)=4b+3

We move all terms to the left:

12-b(5b-9)-(4b+3)=0

We multiply parentheses

-5b^2+9b-(4b+3)+12=0

We get rid of parentheses

-5b^2+9b-4b-3+12=0

We add all the numbers together, and all the variables

-5b^2+5b+9=0

a = -5; b = 5; c = +9;
Δ = b2-4ac
Δ = 52-4·(-5)·9
Δ = 205
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{-(5)-\sqrt{205}}{2*-5}=\frac{-5-\sqrt{205}}{-10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{205}}{2*-5}=\frac{-5+\sqrt{205}}{-10}
$