/5x+3=15-x

Solution for /5x+3=15-x equation:

/5x+3=15-x

We move all terms to the left:

/5x+3-(15-x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

/5x-(-1x+15)+3=0

We get rid of parentheses

/5x+1x-15+3=0

We multiply all the terms by the denominator


1x*5x-15*5x+3*5x+=0

We add all the numbers together, and all the variables

1x*5x-15*5x+3*5x=0

Wy multiply elements

5x^2-75x+15x=0

We add all the numbers together, and all the variables

5x^2-60x=0

a = 5; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·5·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*5}=\frac{120}{10}
=12
$