x=-5/6x+120

Solution for x=-5/6x+120 equation:

x=-5/6x+120

We move all terms to the left:

x-(-5/6x+120)=0


Domain of the equation: 6x+120)!=0

x∈R


We get rid of parentheses

x+5/6x-120=0

We multiply all the terms by the denominator


x*6x-120*6x+5=0

Wy multiply elements

6x^2-720x+5=0

a = 6; b = -720; c = +5;
Δ = b2-4ac
Δ = -7202-4·6·5
Δ = 518280
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:

$\sqrt{\Delta}=\sqrt{518280}=\sqrt{4*129570}=\sqrt{4}*\sqrt{129570}=2\sqrt{129570}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-2\sqrt{129570}}{2*6}=\frac{720-2\sqrt{129570}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+2\sqrt{129570}}{2*6}=\frac{720+2\sqrt{129570}}{12}
$