4x+8/5x+8=56

Solution for 4x+8/5x+8=56 equation:

4x+8/5x+8=56

We move all terms to the left:

4x+8/5x+8-(56)=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+8/5x-48=0

We multiply all the terms by the denominator


4x*5x-48*5x+8=0

Wy multiply elements

20x^2-240x+8=0

a = 20; b = -240; c = +8;
Δ = b2-4ac
Δ = -2402-4·20·8
Δ = 56960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{56960}=\sqrt{64*890}=\sqrt{64}*\sqrt{890}=8\sqrt{890}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-8\sqrt{890}}{2*20}=\frac{240-8\sqrt{890}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+8\sqrt{890}}{2*20}=\frac{240+8\sqrt{890}}{40}
$