4/5x-5/2=9/10x-7

Solution for 4/5x-5/2=9/10x-7 equation:

4/5x-5/2=9/10x-7

We move all terms to the left:

4/5x-5/2-(9/10x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-7)!=0

x∈R


We get rid of parentheses

4/5x-9/10x+7-5/2=0

We calculate fractions


(-250x^2)/200x^2+160x/200x^2+(-180x)/200x^2+7=0

We multiply all the terms by the denominator


(-250x^2)+160x+(-180x)+7*200x^2=0

Wy multiply elements

(-250x^2)+1400x^2+160x+(-180x)=0

We get rid of parentheses

-250x^2+1400x^2+160x-180x=0

We add all the numbers together, and all the variables

1150x^2-20x=0

a = 1150; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·1150·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*1150}=\frac{0}{2300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*1150}=\frac{40}{2300}
=2/115
$