4x-5/2x=10

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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} $

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