2/5x-7=12/5x-2x+13

Solution for 2/5x-7=12/5x-2x+13 equation:

2/5x-7=12/5x-2x+13

We move all terms to the left:

2/5x-7-(12/5x-2x+13)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x-2x+13)!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(-2x+12/5x+13)-7=0

We get rid of parentheses

2/5x+2x-12/5x-13-7=0

We multiply all the terms by the denominator


2x*5x-13*5x-7*5x+2-12=0

We add all the numbers together, and all the variables

2x*5x-13*5x-7*5x-10=0

Wy multiply elements

10x^2-65x-35x-10=0

We add all the numbers together, and all the variables

10x^2-100x-10=0

a = 10; b = -100; c = -10;
Δ = b2-4ac
Δ = -1002-4·10·(-10)
Δ = 10400
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:

$\sqrt{\Delta}=\sqrt{10400}=\sqrt{400*26}=\sqrt{400}*\sqrt{26}=20\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{26}}{2*10}=\frac{100-20\sqrt{26}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{26}}{2*10}=\frac{100+20\sqrt{26}}{20}
$