6/5x-6=x+7

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

6/5x-6=x+7

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

6/5x-x-7-6=0

We multiply all the terms by the denominator


-x*5x-7*5x-6*5x+6=0

Wy multiply elements

-5x^2-35x-30x+6=0

We add all the numbers together, and all the variables

-5x^2-65x+6=0

a = -5; b = -65; c = +6;
Δ = b2-4ac
Δ = -652-4·(-5)·6
Δ = 4345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{4345}}{2*-5}=\frac{65-\sqrt{4345}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4345}}{2*-5}=\frac{65+\sqrt{4345}}{-10}
$