9+3/4w=7/8w-10

Solution for 9+3/4w=7/8w-10 equation:

9+3/4w=7/8w-10

We move all terms to the left:

9+3/4w-(7/8w-10)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 8w-10)!=0

w∈R


We get rid of parentheses

3/4w-7/8w+10+9=0

We calculate fractions


24w/32w^2+(-28w)/32w^2+10+9=0

We add all the numbers together, and all the variables

24w/32w^2+(-28w)/32w^2+19=0

We multiply all the terms by the denominator


24w+(-28w)+19*32w^2=0

Wy multiply elements

608w^2+24w+(-28w)=0

We get rid of parentheses

608w^2+24w-28w=0

We add all the numbers together, and all the variables

608w^2-4w=0

a = 608; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·608·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*608}=\frac{0}{1216}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*608}=\frac{8}{1216}
=1/152
$