8/10b=4/2b-7

Solution for 8/10b=4/2b-7 equation:

8/10b=4/2b-7

We move all terms to the left:

8/10b-(4/2b-7)=0


Domain of the equation: 10b!=0

b!=0/10

b!=0

b∈R



Domain of the equation: 2b-7)!=0

b∈R


We get rid of parentheses

8/10b-4/2b+7=0

We calculate fractions


16b/20b^2+(-40b)/20b^2+7=0

We multiply all the terms by the denominator


16b+(-40b)+7*20b^2=0

Wy multiply elements

140b^2+16b+(-40b)=0

We get rid of parentheses

140b^2+16b-40b=0

We add all the numbers together, and all the variables

140b^2-24b=0

a = 140; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·140·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*140}=\frac{0}{280}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*140}=\frac{48}{280}
=6/35
$