4/5x-2/3=7/10x-2

Solution for 4/5x-2/3=7/10x-2 equation:

4/5x-2/3=7/10x-2

We move all terms to the left:

4/5x-2/3-(7/10x-2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-2)!=0

x∈R


We get rid of parentheses

4/5x-7/10x+2-2/3=0

We calculate fractions


(-100x^2)/450x^2+360x/450x^2+(-315x)/450x^2+2=0

We multiply all the terms by the denominator


(-100x^2)+360x+(-315x)+2*450x^2=0

Wy multiply elements

(-100x^2)+900x^2+360x+(-315x)=0

We get rid of parentheses

-100x^2+900x^2+360x-315x=0

We add all the numbers together, and all the variables

800x^2+45x=0

a = 800; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·800·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*800}=\frac{-90}{1600}
=-9/160
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*800}=\frac{0}{1600}
=0
$