X-10+2x-67+1/2x+5=180

Solution for X-10+2x-67+1/2x+5=180 equation:

X-10+2X-67+1/2X+5=180

We move all terms to the left:

X-10+2X-67+1/2X+5-(180)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

3X+1/2X-252=0

We multiply all the terms by the denominator


3X*2X-252*2X+1=0

Wy multiply elements

6X^2-504X+1=0

a = 6; b = -504; c = +1;
Δ = b2-4ac
Δ = -5042-4·6·1
Δ = 253992
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:

$\sqrt{\Delta}=\sqrt{253992}=\sqrt{4*63498}=\sqrt{4}*\sqrt{63498}=2\sqrt{63498}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-504)-2\sqrt{63498}}{2*6}=\frac{504-2\sqrt{63498}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-504)+2\sqrt{63498}}{2*6}=\frac{504+2\sqrt{63498}}{12}
$