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 get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-10x^2+15x+6=0

a = -10; b = 15; c = +6;
Δ = b2-4ac
Δ = 152-4·(-10)·6
Δ = 465
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{-(15)-\sqrt{465}}{2*-10}=\frac{-15-\sqrt{465}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{465}}{2*-10}=\frac{-15+\sqrt{465}}{-20}
$