-b(13+4b)=-3(5-9b)+2

Solution for -b(13+4b)=-3(5-9b)+2 equation:

-b(13+4b)=-3(5-9b)+2

We move all terms to the left:

-b(13+4b)-(-3(5-9b)+2)=0

We add all the numbers together, and all the variables

-b(4b+13)-(-3(-9b+5)+2)=0

We multiply parentheses

-4b^2-13b-(-3(-9b+5)+2)=0


We calculate terms in parentheses: -(-3(-9b+5)+2), so:

-3(-9b+5)+2

We multiply parentheses

27b-15+2

We add all the numbers together, and all the variables

27b-13

Back to the equation:

-(27b-13)


We get rid of parentheses

-4b^2-13b-27b+13=0

We add all the numbers together, and all the variables

-4b^2-40b+13=0

a = -4; b = -40; c = +13;
Δ = b2-4ac
Δ = -402-4·(-4)·13
Δ = 1808
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1808}=\sqrt{16*113}=\sqrt{16}*\sqrt{113}=4\sqrt{113}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{113}}{2*-4}=\frac{40-4\sqrt{113}}{-8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{113}}{2*-4}=\frac{40+4\sqrt{113}}{-8}
$