3x+(15)/(x+4)=7

Solution for 3x+(15)/(x+4)=7 equation:

3x+(15)/(x+4)=7

We move all terms to the left:

3x+(15)/(x+4)-(7)=0


Domain of the equation: (x+4)!=0

We move all terms containing x to the left, all other terms to the right

x!=-4

x∈R


We multiply all the terms by the denominator


3x*(x+4)-7*(x+4)+15=0

We multiply parentheses

3x^2+12x-7x-28+15=0

We add all the numbers together, and all the variables

3x^2+5x-13=0

a = 3; b = 5; c = -13;
Δ = b2-4ac
Δ = 52-4·3·(-13)
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{181}}{2*3}=\frac{-5-\sqrt{181}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{181}}{2*3}=\frac{-5+\sqrt{181}}{6}
$