10/x+4=30/2x+3

Solution for 10/x+4=30/2x+3 equation:

10/x+4=30/2x+3

We move all terms to the left:

10/x+4-(30/2x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

10/x-30/2x-3+4=0

We calculate fractions


20x/2x^2+(-30x)/2x^2-3+4=0

We add all the numbers together, and all the variables

20x/2x^2+(-30x)/2x^2+1=0

We multiply all the terms by the denominator


20x+(-30x)+1*2x^2=0

Wy multiply elements

2x^2+20x+(-30x)=0

We get rid of parentheses

2x^2+20x-30x=0

We add all the numbers together, and all the variables

2x^2-10x=0

a = 2; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·2·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*2}=\frac{20}{4}
=5
$