180=3x+17+1/2x-5

Solution for 180=3x+17+1/2x-5 equation:

180=3x+17+1/2x-5

We move all terms to the left:

180-(3x+17+1/2x-5)=0


Domain of the equation: 2x-5)!=0

x∈R


We add all the numbers together, and all the variables

-(3x+1/2x+12)+180=0

We get rid of parentheses

-3x-1/2x-12+180=0

We multiply all the terms by the denominator


-3x*2x-12*2x+180*2x-1=0

Wy multiply elements

-6x^2-24x+360x-1=0

We add all the numbers together, and all the variables

-6x^2+336x-1=0

a = -6; b = 336; c = -1;
Δ = b2-4ac
Δ = 3362-4·(-6)·(-1)
Δ = 112872
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:

$\sqrt{\Delta}=\sqrt{112872}=\sqrt{4*28218}=\sqrt{4}*\sqrt{28218}=2\sqrt{28218}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(336)-2\sqrt{28218}}{2*-6}=\frac{-336-2\sqrt{28218}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(336)+2\sqrt{28218}}{2*-6}=\frac{-336+2\sqrt{28218}}{-12}
$