5/2x-18=4x

Solution for 5/2x-18=4x equation:

5/2x-18=4x

We move all terms to the left:

5/2x-18-(4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+5/2x-18=0

We multiply all the terms by the denominator


-4x*2x-18*2x+5=0

Wy multiply elements

-8x^2-36x+5=0

a = -8; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·(-8)·5
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{91}}{2*-8}=\frac{36-4\sqrt{91}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{91}}{2*-8}=\frac{36+4\sqrt{91}}{-16}
$