5x-30+5/2x-15=180

Solution for 5x-30+5/2x-15=180 equation:

5x-30+5/2x-15=180

We move all terms to the left:

5x-30+5/2x-15-(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+5/2x-225=0

We multiply all the terms by the denominator


5x*2x-225*2x+5=0

Wy multiply elements

10x^2-450x+5=0

a = 10; b = -450; c = +5;
Δ = b2-4ac
Δ = -4502-4·10·5
Δ = 202300
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:

$\sqrt{\Delta}=\sqrt{202300}=\sqrt{28900*7}=\sqrt{28900}*\sqrt{7}=170\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-170\sqrt{7}}{2*10}=\frac{450-170\sqrt{7}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+170\sqrt{7}}{2*10}=\frac{450+170\sqrt{7}}{20}
$