5/6x+15=x-5

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

5/6x+15=x-5

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+30x+90x+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}
$