3/4b+4=1/2b+10

Solution for 3/4b+4=1/2b+10 equation:

3/4b+4=1/2b+10

We move all terms to the left:

3/4b+4-(1/2b+10)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 2b+10)!=0

b∈R


We get rid of parentheses

3/4b-1/2b-10+4=0

We calculate fractions


6b/8b^2+(-4b)/8b^2-10+4=0

We add all the numbers together, and all the variables

6b/8b^2+(-4b)/8b^2-6=0

We multiply all the terms by the denominator


6b+(-4b)-6*8b^2=0

Wy multiply elements

-48b^2+6b+(-4b)=0

We get rid of parentheses

-48b^2+6b-4b=0

We add all the numbers together, and all the variables

-48b^2+2b=0

a = -48; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-48)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-48}=\frac{-4}{-96}
=1/24
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-48}=\frac{0}{-96}
=0
$