x-5=5/6x+15

Solution for x-5=5/6x+15 equation:

x-5=5/6x+15

We move all terms to the left:

x-5-(5/6x+15)=0


Domain of the equation: 6x+15)!=0

x∈R


We get rid of parentheses

x-5/6x-15-5=0

We multiply all the terms by the denominator


x*6x-15*6x-5*6x-5=0

Wy multiply elements

6x^2-90x-30x-5=0

We add all the numbers together, and all the variables

6x^2-120x-5=0

a = 6; b = -120; c = -5;
Δ = b2-4ac
Δ = -1202-4·6·(-5)
Δ = 14520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14520}=\sqrt{484*30}=\sqrt{484}*\sqrt{30}=22\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-22\sqrt{30}}{2*6}=\frac{120-22\sqrt{30}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+22\sqrt{30}}{2*6}=\frac{120+22\sqrt{30}}{12}
$