2/5x-7=1.3x-6

Solution for 2/5x-7=1.3x-6 equation:

2/5x-7=1.3x-6

We move all terms to the left:

2/5x-7-(1.3x-6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-1.3x+6-7=0

We multiply all the terms by the denominator


-(1.3x)*5x+6*5x-7*5x+2=0

We add all the numbers together, and all the variables

-(+1.3x)*5x+6*5x-7*5x+2=0

We multiply parentheses

-5x^2+6*5x-7*5x+2=0

Wy multiply elements

-5x^2+30x-35x+2=0

We add all the numbers together, and all the variables

-5x^2-5x+2=0

a = -5; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-5)·2
Δ = 65
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{-(-5)-\sqrt{65}}{2*-5}=\frac{5-\sqrt{65}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*-5}=\frac{5+\sqrt{65}}{-10}
$