1/2x-4/5=5/6x+8

Solution for 1/2x-4/5=5/6x+8 equation:

1/2x-4/5=5/6x+8

We move all terms to the left:

1/2x-4/5-(5/6x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+8)!=0

x∈R


We get rid of parentheses

1/2x-5/6x-8-4/5=0

We calculate fractions


(-288x^2)/300x^2+150x/300x^2+(-250x)/300x^2-8=0

We multiply all the terms by the denominator


(-288x^2)+150x+(-250x)-8*300x^2=0

Wy multiply elements

(-288x^2)-2400x^2+150x+(-250x)=0

We get rid of parentheses

-288x^2-2400x^2+150x-250x=0

We add all the numbers together, and all the variables

-2688x^2-100x=0

a = -2688; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·(-2688)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*-2688}=\frac{0}{-5376}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*-2688}=\frac{200}{-5376}
=-25/672
$