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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

6/5x-(2x-13)=0

We get rid of parentheses

6/5x-2x+13=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -10; b = 65; c = +6;
Δ = b2-4ac
Δ = 652-4·(-10)·6
Δ = 4465
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{-(65)-\sqrt{4465}}{2*-10}=\frac{-65-\sqrt{4465}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4465}}{2*-10}=\frac{-65+\sqrt{4465}}{-20}
$