5b(2+4b)=2(6-2b)

Solution for 5b(2+4b)=2(6-2b) equation:

5b(2+4b)=2(6-2b)

We move all terms to the left:

5b(2+4b)-(2(6-2b))=0

We add all the numbers together, and all the variables

5b(4b+2)-(2(-2b+6))=0

We multiply parentheses

20b^2+10b-(2(-2b+6))=0


We calculate terms in parentheses: -(2(-2b+6)), so:

2(-2b+6)

We multiply parentheses

-4b+12

Back to the equation:

-(-4b+12)


We get rid of parentheses

20b^2+10b+4b-12=0

We add all the numbers together, and all the variables

20b^2+14b-12=0

a = 20; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·20·(-12)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-34}{2*20}=\frac{-48}{40}
=-1+1/5
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+34}{2*20}=\frac{20}{40}
=1/2
$