2/3x-7=5/8x+8

Solution for 2/3x-7=5/8x+8 equation:

2/3x-7=5/8x+8

We move all terms to the left:

2/3x-7-(5/8x+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-5/8x-8-7=0

We calculate fractions


16x/24x^2+(-15x)/24x^2-8-7=0

We add all the numbers together, and all the variables

16x/24x^2+(-15x)/24x^2-15=0

We multiply all the terms by the denominator


16x+(-15x)-15*24x^2=0

Wy multiply elements

-360x^2+16x+(-15x)=0

We get rid of parentheses

-360x^2+16x-15x=0

We add all the numbers together, and all the variables

-360x^2+x=0

a = -360; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-360)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-360}=\frac{-2}{-720}
=1/360
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-360}=\frac{0}{-720}
=0
$