4x-294+x-26+1/2x+16=180

Solution for 4x-294+x-26+1/2x+16=180 equation:

4x-294+x-26+1/2x+16=180

We move all terms to the left:

4x-294+x-26+1/2x+16-(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

5x+1/2x-484=0

We multiply all the terms by the denominator


5x*2x-484*2x+1=0

Wy multiply elements

10x^2-968x+1=0

a = 10; b = -968; c = +1;
Δ = b2-4ac
Δ = -9682-4·10·1
Δ = 936984
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:

$\sqrt{\Delta}=\sqrt{936984}=\sqrt{4*234246}=\sqrt{4}*\sqrt{234246}=2\sqrt{234246}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-968)-2\sqrt{234246}}{2*10}=\frac{968-2\sqrt{234246}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-968)+2\sqrt{234246}}{2*10}=\frac{968+2\sqrt{234246}}{20}
$