10/x+3=20-3x

Solution for 10/x+3=20-3x equation:

10/x+3=20-3x

We move all terms to the left:

10/x+3-(20-3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

10/x-(-3x+20)+3=0

We get rid of parentheses

10/x+3x-20+3=0

We multiply all the terms by the denominator


3x*x-20*x+3*x+10=0

We add all the numbers together, and all the variables

-17x+3x*x+10=0

Wy multiply elements

3x^2-17x+10=0

a = 3; b = -17; c = +10;
Δ = b2-4ac
Δ = -172-4·3·10
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*3}=\frac{4}{6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*3}=\frac{30}{6}
=5
$