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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-80x^2)/1000x^2+750x/1000x^2+(-700x)/1000x^2-2=0

We multiply all the terms by the denominator


(-80x^2)+750x+(-700x)-2*1000x^2=0

Wy multiply elements

(-80x^2)-2000x^2+750x+(-700x)=0

We get rid of parentheses

-80x^2-2000x^2+750x-700x=0

We add all the numbers together, and all the variables

-2080x^2+50x=0

a = -2080; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-2080)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-2080}=\frac{-100}{-4160}
=5/208
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-2080}=\frac{0}{-4160}
=0
$