-8b(3b-7)=-4-2(b+3)

Solution for -8b(3b-7)=-4-2(b+3) equation:

-8b(3b-7)=-4-2(b+3)

We move all terms to the left:

-8b(3b-7)-(-4-2(b+3))=0

We multiply parentheses

-24b^2+56b-(-4-2(b+3))=0


We calculate terms in parentheses: -(-4-2(b+3)), so:

-4-2(b+3)

determiningTheFunctionDomain
-2(b+3)-4

We multiply parentheses

-2b-6-4

We add all the numbers together, and all the variables

-2b-10

Back to the equation:

-(-2b-10)


We get rid of parentheses

-24b^2+56b+2b+10=0

We add all the numbers together, and all the variables

-24b^2+58b+10=0

a = -24; b = 58; c = +10;
Δ = b2-4ac
Δ = 582-4·(-24)·10
Δ = 4324
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:

$\sqrt{\Delta}=\sqrt{4324}=\sqrt{4*1081}=\sqrt{4}*\sqrt{1081}=2\sqrt{1081}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{1081}}{2*-24}=\frac{-58-2\sqrt{1081}}{-48}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{1081}}{2*-24}=\frac{-58+2\sqrt{1081}}{-48}
$