1/3x-60=2x-10

Solution for 1/3x-60=2x-10 equation:

1/3x-60=2x-10

We move all terms to the left:

1/3x-60-(2x-10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x+10-60=0

We multiply all the terms by the denominator


-2x*3x+10*3x-60*3x+1=0

Wy multiply elements

-6x^2+30x-180x+1=0

We add all the numbers together, and all the variables

-6x^2-150x+1=0

a = -6; b = -150; c = +1;
Δ = b2-4ac
Δ = -1502-4·(-6)·1
Δ = 22524
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:

$\sqrt{\Delta}=\sqrt{22524}=\sqrt{4*5631}=\sqrt{4}*\sqrt{5631}=2\sqrt{5631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5631}}{2*-6}=\frac{150-2\sqrt{5631}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5631}}{2*-6}=\frac{150+2\sqrt{5631}}{-12}
$