5x-5/2x+10=180

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

5x-5/2x+10=180

We move all terms to the left:

5x-5/2x+10-(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-170=0

We multiply all the terms by the denominator


5x*2x-170*2x-5=0

Wy multiply elements

10x^2-340x-5=0

a = 10; b = -340; c = -5;
Δ = b2-4ac
Δ = -3402-4·10·(-5)
Δ = 115800
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:

$\sqrt{\Delta}=\sqrt{115800}=\sqrt{100*1158}=\sqrt{100}*\sqrt{1158}=10\sqrt{1158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-340)-10\sqrt{1158}}{2*10}=\frac{340-10\sqrt{1158}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-340)+10\sqrt{1158}}{2*10}=\frac{340+10\sqrt{1158}}{20}
$