9/10x+30=3/5x

Solution for 9/10x+30=3/5x equation:

9/10x+30=3/5x

We move all terms to the left:

9/10x+30-(3/5x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/10x-(+3/5x)+30=0

We get rid of parentheses

9/10x-3/5x+30=0

We calculate fractions


45x/50x^2+(-30x)/50x^2+30=0

We multiply all the terms by the denominator


45x+(-30x)+30*50x^2=0

Wy multiply elements

1500x^2+45x+(-30x)=0

We get rid of parentheses

1500x^2+45x-30x=0

We add all the numbers together, and all the variables

1500x^2+15x=0

a = 1500; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·1500·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*1500}=\frac{-30}{3000}
=-1/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*1500}=\frac{0}{3000}
=0
$