3/4x-1/2=7/10x

Solution for 3/4x-1/2=7/10x equation:

3/4x-1/2=7/10x

We move all terms to the left:

3/4x-1/2-(7/10x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(+7/10x)-1/2=0

We get rid of parentheses

3/4x-7/10x-1/2=0

We calculate fractions


(-40x^2)/160x^2+120x/160x^2+(-112x)/160x^2=0

We multiply all the terms by the denominator


(-40x^2)+120x+(-112x)=0

We get rid of parentheses

-40x^2+120x-112x=0

We add all the numbers together, and all the variables

-40x^2+8x=0

a = -40; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-40)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-40}=\frac{-16}{-80}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-40}=\frac{0}{-80}
=0
$