x+20+1/2x-35+4x-25=180

Solution for x+20+1/2x-35+4x-25=180 equation:

x+20+1/2x-35+4x-25=180

We move all terms to the left:

x+20+1/2x-35+4x-25-(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-220=0

We multiply all the terms by the denominator


5x*2x-220*2x+1=0

Wy multiply elements

10x^2-440x+1=0

a = 10; b = -440; c = +1;
Δ = b2-4ac
Δ = -4402-4·10·1
Δ = 193560
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:

$\sqrt{\Delta}=\sqrt{193560}=\sqrt{4*48390}=\sqrt{4}*\sqrt{48390}=2\sqrt{48390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-440)-2\sqrt{48390}}{2*10}=\frac{440-2\sqrt{48390}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-440)+2\sqrt{48390}}{2*10}=\frac{440+2\sqrt{48390}}{20}
$