(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+18)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-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}
$