180-x=3/2x-10

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

180-x=3/2x-10

We move all terms to the left:

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


Domain of the equation: 2x-10)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(3/2x-10)+180=0

We get rid of parentheses

-1x-3/2x+10+180=0

We multiply all the terms by the denominator


-1x*2x+10*2x+180*2x-3=0

Wy multiply elements

-2x^2+20x+360x-3=0

We add all the numbers together, and all the variables

-2x^2+380x-3=0

a = -2; b = 380; c = -3;
Δ = b2-4ac
Δ = 3802-4·(-2)·(-3)
Δ = 144376
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:

$\sqrt{\Delta}=\sqrt{144376}=\sqrt{4*36094}=\sqrt{4}*\sqrt{36094}=2\sqrt{36094}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(380)-2\sqrt{36094}}{2*-2}=\frac{-380-2\sqrt{36094}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(380)+2\sqrt{36094}}{2*-2}=\frac{-380+2\sqrt{36094}}{-4}
$