5/2x=4x-9

Solution for 5/2x=4x-9 equation:

5/2x=4x-9

We move all terms to the left:

5/2x-(4x-9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-4x+9=0

We multiply all the terms by the denominator


-4x*2x+9*2x+5=0

Wy multiply elements

-8x^2+18x+5=0

a = -8; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·(-8)·5
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-22}{2*-8}=\frac{-40}{-16}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+22}{2*-8}=\frac{4}{-16}
=-1/4
$