10x-5/2x-4=0

Solution for 10x-5/2x-4=0 equation:

10x-5/2x-4=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

20x^2-8x-5=0

a = 20; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·20·(-5)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{29}}{2*20}=\frac{8-4\sqrt{29}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{29}}{2*20}=\frac{8+4\sqrt{29}}{40}
$