2x+(1/2x+25)=180

Solution for 2x+(1/2x+25)=180 equation:

2x+(1/2x+25)=180

We move all terms to the left:

2x+(1/2x+25)-(180)=0


Domain of the equation: 2x+25)!=0

x∈R


We get rid of parentheses

2x+1/2x+25-180=0

We multiply all the terms by the denominator


2x*2x+25*2x-180*2x+1=0

Wy multiply elements

4x^2+50x-360x+1=0

We add all the numbers together, and all the variables

4x^2-310x+1=0

a = 4; b = -310; c = +1;
Δ = b2-4ac
Δ = -3102-4·4·1
Δ = 96084
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:

$\sqrt{\Delta}=\sqrt{96084}=\sqrt{36*2669}=\sqrt{36}*\sqrt{2669}=6\sqrt{2669}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-310)-6\sqrt{2669}}{2*4}=\frac{310-6\sqrt{2669}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-310)+6\sqrt{2669}}{2*4}=\frac{310+6\sqrt{2669}}{8}
$