(6/5x+10)+(2x-13)=180

Solution for (6/5x+10)+(2x-13)=180 equation:

(6/5x+10)+(2x-13)=180

We move all terms to the left:

(6/5x+10)+(2x-13)-(180)=0


Domain of the equation: 5x+10)!=0

x∈R


We get rid of parentheses

6/5x+2x+10-13-180=0

We multiply all the terms by the denominator


2x*5x+10*5x-13*5x-180*5x+6=0

Wy multiply elements

10x^2+50x-65x-900x+6=0

We add all the numbers together, and all the variables

10x^2-915x+6=0

a = 10; b = -915; c = +6;
Δ = b2-4ac
Δ = -9152-4·10·6
Δ = 836985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-915)-\sqrt{836985}}{2*10}=\frac{915-\sqrt{836985}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-915)+\sqrt{836985}}{2*10}=\frac{915+\sqrt{836985}}{20}
$