7/2b+5=9/4b+6

Solution for 7/2b+5=9/4b+6 equation:

7/2b+5=9/4b+6

We move all terms to the left:

7/2b+5-(9/4b+6)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 4b+6)!=0

b∈R


We get rid of parentheses

7/2b-9/4b-6+5=0

We calculate fractions


28b/8b^2+(-18b)/8b^2-6+5=0

We add all the numbers together, and all the variables

28b/8b^2+(-18b)/8b^2-1=0

We multiply all the terms by the denominator


28b+(-18b)-1*8b^2=0

Wy multiply elements

-8b^2+28b+(-18b)=0

We get rid of parentheses

-8b^2+28b-18b=0

We add all the numbers together, and all the variables

-8b^2+10b=0

a = -8; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-8)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-8}=\frac{-20}{-16}
=1+1/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-8}=\frac{0}{-16}
=0
$