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

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

X+3/2X+(X-10)=180

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4X^2-380X+3=0

a = 4; b = -380; c = +3;
Δ = b2-4ac
Δ = -3802-4·4·3
Δ = 144352
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:

$\sqrt{\Delta}=\sqrt{144352}=\sqrt{16*9022}=\sqrt{16}*\sqrt{9022}=4\sqrt{9022}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-4\sqrt{9022}}{2*4}=\frac{380-4\sqrt{9022}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+4\sqrt{9022}}{2*4}=\frac{380+4\sqrt{9022}}{8}
$