4x=5/2x+18

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

4x=5/2x+18

We move all terms to the left:

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


Domain of the equation: 2x+18)!=0

x∈R


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}
$