2x+6/4x=10

Solution for 2x+6/4x=10 equation:

2x+6/4x=10

We move all terms to the left:

2x+6/4x-(10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-10*4x+6=0

Wy multiply elements

8x^2-40x+6=0

a = 8; b = -40; c = +6;
Δ = b2-4ac
Δ = -402-4·8·6
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{22}}{2*8}=\frac{40-8\sqrt{22}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{22}}{2*8}=\frac{40+8\sqrt{22}}{16}
$