180=2/3x+x-10

Solution for 180=2/3x+x-10 equation:

180=2/3x+x-10

We move all terms to the left:

180-(2/3x+x-10)=0


Domain of the equation: 3x+x-10)!=0

x∈R


We add all the numbers together, and all the variables

-(x+2/3x-10)+180=0

We get rid of parentheses

-x-2/3x+10+180=0

We multiply all the terms by the denominator


-x*3x+10*3x+180*3x-2=0

Wy multiply elements

-3x^2+30x+540x-2=0

We add all the numbers together, and all the variables

-3x^2+570x-2=0

a = -3; b = 570; c = -2;
Δ = b2-4ac
Δ = 5702-4·(-3)·(-2)
Δ = 324876
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:

$\sqrt{\Delta}=\sqrt{324876}=\sqrt{4*81219}=\sqrt{4}*\sqrt{81219}=2\sqrt{81219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(570)-2\sqrt{81219}}{2*-3}=\frac{-570-2\sqrt{81219}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(570)+2\sqrt{81219}}{2*-3}=\frac{-570+2\sqrt{81219}}{-6}
$