8x-10/2x=4

Solution for 8x-10/2x=4 equation:

8x-10/2x=4

We move all terms to the left:

8x-10/2x-(4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


8x*2x-4*2x-10=0

Wy multiply elements

16x^2-8x-10=0

a = 16; b = -8; c = -10;
Δ = b2-4ac
Δ = -82-4·16·(-10)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{11}}{2*16}=\frac{8-8\sqrt{11}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{11}}{2*16}=\frac{8+8\sqrt{11}}{32}
$