X/5x+15=3x+21

Solution for X/5x+15=3x+21 equation:

X/5X+15=3X+21

We move all terms to the left:

X/5X+15-(3X+21)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We get rid of parentheses

X/5X-3X-21+15=0

We multiply all the terms by the denominator


X-3X*5X-21*5X+15*5X=0

Wy multiply elements

-15X^2+X-105X+75X=0

We add all the numbers together, and all the variables

-15X^2-29X=0

a = -15; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·(-15)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*-15}=\frac{0}{-30}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*-15}=\frac{58}{-30}
=-1+14/15
$