5x-9/2x=1

Solution for 5x-9/2x=1 equation:

5x-9/2x=1

We move all terms to the left:

5x-9/2x-(1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


5x*2x-1*2x-9=0

Wy multiply elements

10x^2-2x-9=0

a = 10; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·10·(-9)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{91}}{2*10}=\frac{2-2\sqrt{91}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{91}}{2*10}=\frac{2+2\sqrt{91}}{20}
$