4x-5/2x=10

Solution for 4x-5/2x=10 equation:

4x-5/2x=10

We move all terms to the left:

4x-5/2x-(10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-10*2x-5=0

Wy multiply elements

8x^2-20x-5=0

a = 8; b = -20; c = -5;
Δ = b2-4ac
Δ = -202-4·8·(-5)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{35}}{2*8}=\frac{20-4\sqrt{35}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{35}}{2*8}=\frac{20+4\sqrt{35}}{16}
$