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!=0

x∈R


We add all the numbers together, and all the variables

4x+8x/x+2=0

We multiply all the terms by the denominator


4x*x+8x+2*x=0

We add all the numbers together, and all the variables

10x+4x*x=0

Wy multiply elements

4x^2+10x=0

a = 4; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·4·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*4}=\frac{0}{8}
=0
$