b/8b+10=3b+25

Solution for b/8b+10=3b+25 equation:

b/8b+10=3b+25

We move all terms to the left:

b/8b+10-(3b+25)=0


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R


We get rid of parentheses

b/8b-3b-25+10=0

We multiply all the terms by the denominator


b-3b*8b-25*8b+10*8b=0

Wy multiply elements

-24b^2+b-200b+80b=0

We add all the numbers together, and all the variables

-24b^2-119b=0

a = -24; b = -119; c = 0;
Δ = b2-4ac
Δ = -1192-4·(-24)·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-119}{2*-24}=\frac{0}{-48}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+119}{2*-24}=\frac{238}{-48}
=-4+23/24
$