4x+8/5x+8=0

Solution for 4x+8/5x+8=0 equation:

4x+8/5x+8=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

20x^2+40x+8=0

a = 20; b = 40; c = +8;
Δ = b2-4ac
Δ = 402-4·20·8
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{15}}{2*20}=\frac{-40-8\sqrt{15}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{15}}{2*20}=\frac{-40+8\sqrt{15}}{40}
$