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

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

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

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


120x^2/500x^2+350x/500x^2+(-750x)/500x^2-2=0

We multiply all the terms by the denominator


120x^2+350x+(-750x)-2*500x^2=0

Wy multiply elements

120x^2-1000x^2+350x+(-750x)=0

We get rid of parentheses

120x^2-1000x^2+350x-750x=0

We add all the numbers together, and all the variables

-880x^2-400x=0

a = -880; b = -400; c = 0;
Δ = b2-4ac
Δ = -4002-4·(-880)·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-400}{2*-880}=\frac{0}{-1760}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+400}{2*-880}=\frac{800}{-1760}
=-5/11
$