9/10x-2/5=3/25x+3

Solution for 9/10x-2/5=3/25x+3 equation:

9/10x-2/5=3/25x+3

We move all terms to the left:

9/10x-2/5-(3/25x+3)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 25x+3)!=0

x∈R


We get rid of parentheses

9/10x-3/25x-3-2/5=0

We calculate fractions


(-1000x^2)/6250x^2+5625x/6250x^2+(-750x)/6250x^2-3=0

We multiply all the terms by the denominator


(-1000x^2)+5625x+(-750x)-3*6250x^2=0

Wy multiply elements

(-1000x^2)-18750x^2+5625x+(-750x)=0

We get rid of parentheses

-1000x^2-18750x^2+5625x-750x=0

We add all the numbers together, and all the variables

-19750x^2+4875x=0

a = -19750; b = 4875; c = 0;
Δ = b2-4ac
Δ = 48752-4·(-19750)·0
Δ = 23765625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23765625}=4875$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4875)-4875}{2*-19750}=\frac{-9750}{-39500}
=39/158
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4875)+4875}{2*-19750}=\frac{0}{-39500}
=0
$