5/6*x=x-240

Solution for 5/6*x=x-240 equation:

5/6x=x-240

We move all terms to the left:

5/6x-(x-240)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

5/6x-x+240=0

We multiply all the terms by the denominator


-x*6x+240*6x+5=0

Wy multiply elements

-6x^2+1440x+5=0

a = -6; b = 1440; c = +5;
Δ = b2-4ac
Δ = 14402-4·(-6)·5
Δ = 2073720
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:

$\sqrt{\Delta}=\sqrt{2073720}=\sqrt{4*518430}=\sqrt{4}*\sqrt{518430}=2\sqrt{518430}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1440)-2\sqrt{518430}}{2*-6}=\frac{-1440-2\sqrt{518430}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1440)+2\sqrt{518430}}{2*-6}=\frac{-1440+2\sqrt{518430}}{-12}
$