X/5x+4x+7=x+15

Solution for X/5x+4x+7=x+15 equation:

X/5X+4X+7=X+15

We move all terms to the left:

X/5X+4X+7-(X+15)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We add all the numbers together, and all the variables

4X+X/5X-(X+15)+7=0

We get rid of parentheses

4X+X/5X-X-15+7=0

We multiply all the terms by the denominator


4X*5X+X-X*5X-15*5X+7*5X=0

We add all the numbers together, and all the variables

X+4X*5X-X*5X-15*5X+7*5X=0

Wy multiply elements

20X^2-5X^2+X-75X+35X=0

We add all the numbers together, and all the variables

15X^2-39X=0

a = 15; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·15·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*15}=\frac{0}{30}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*15}=\frac{78}{30}
=2+3/5
$