5/6x+6=7/4x-8

Solution for 5/6x+6=7/4x-8 equation:

5/6x+6=7/4x-8

We move all terms to the left:

5/6x+6-(7/4x-8)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x-8)!=0

x∈R


We get rid of parentheses

5/6x-7/4x+8+6=0

We calculate fractions


20x/24x^2+(-42x)/24x^2+8+6=0

We add all the numbers together, and all the variables

20x/24x^2+(-42x)/24x^2+14=0

We multiply all the terms by the denominator


20x+(-42x)+14*24x^2=0

Wy multiply elements

336x^2+20x+(-42x)=0

We get rid of parentheses

336x^2+20x-42x=0

We add all the numbers together, and all the variables

336x^2-22x=0

a = 336; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·336·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*336}=\frac{0}{672}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*336}=\frac{44}{672}
=11/168
$