7/10x-8=1/5x-6

Solution for 7/10x-8=1/5x-6 equation:

7/10x-8=1/5x-6

We move all terms to the left:

7/10x-8-(1/5x-6)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x-6)!=0

x∈R


We get rid of parentheses

7/10x-1/5x+6-8=0

We calculate fractions


35x/50x^2+(-10x)/50x^2+6-8=0

We add all the numbers together, and all the variables

35x/50x^2+(-10x)/50x^2-2=0

We multiply all the terms by the denominator


35x+(-10x)-2*50x^2=0

Wy multiply elements

-100x^2+35x+(-10x)=0

We get rid of parentheses

-100x^2+35x-10x=0

We add all the numbers together, and all the variables

-100x^2+25x=0

a = -100; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-100)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-100}=\frac{-50}{-200}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-100}=\frac{0}{-200}
=0
$