2/3x+12=7/8x-8

Solution for 2/3x+12=7/8x-8 equation:

2/3x+12=7/8x-8

We move all terms to the left:

2/3x+12-(7/8x-8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 8x-8)!=0

x∈R


We get rid of parentheses

2/3x-7/8x+8+12=0

We calculate fractions


16x/24x^2+(-21x)/24x^2+8+12=0

We add all the numbers together, and all the variables

16x/24x^2+(-21x)/24x^2+20=0

We multiply all the terms by the denominator


16x+(-21x)+20*24x^2=0

Wy multiply elements

480x^2+16x+(-21x)=0

We get rid of parentheses

480x^2+16x-21x=0

We add all the numbers together, and all the variables

480x^2-5x=0

a = 480; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·480·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*480}=\frac{0}{960}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*480}=\frac{10}{960}
=1/96
$