4x+5/8x+5x=10

Solution for 4x+5/8x+5x=10 equation:

4x+5/8x+5x=10

We move all terms to the left:

4x+5/8x+5x-(10)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

9x+5/8x-10=0

We multiply all the terms by the denominator


9x*8x-10*8x+5=0

Wy multiply elements

72x^2-80x+5=0

a = 72; b = -80; c = +5;
Δ = b2-4ac
Δ = -802-4·72·5
Δ = 4960
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:

$\sqrt{\Delta}=\sqrt{4960}=\sqrt{16*310}=\sqrt{16}*\sqrt{310}=4\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{310}}{2*72}=\frac{80-4\sqrt{310}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{310}}{2*72}=\frac{80+4\sqrt{310}}{144}
$