8X/(x+7)+4x=5

Solution for 8X/(x+7)+4x=5 equation:

8X/(X+7)+4X=5

We move all terms to the left:

8X/(X+7)+4X-(5)=0


Domain of the equation: (X+7)!=0

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

X!=-7

X∈R


We add all the numbers together, and all the variables

4X+8X/(X+7)-5=0

We multiply all the terms by the denominator


4X*(X+7)+8X-5*(X+7)=0

We add all the numbers together, and all the variables

8X+4X*(X+7)-5*(X+7)=0

We multiply parentheses

4X^2+8X+28X-5X-35=0

We add all the numbers together, and all the variables

4X^2+31X-35=0

a = 4; b = 31; c = -35;
Δ = b2-4ac
Δ = 312-4·4·(-35)
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{-(31)-39}{2*4}=\frac{-70}{8}
=-8+3/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+39}{2*4}=\frac{8}{8}
=1
$