4x=5/2x+33

Solution for 4x=5/2x+33 equation:

4x=5/2x+33

We move all terms to the left:

4x-(5/2x+33)=0


Domain of the equation: 2x+33)!=0

x∈R


We get rid of parentheses

4x-5/2x-33=0

We multiply all the terms by the denominator


4x*2x-33*2x-5=0

Wy multiply elements

8x^2-66x-5=0

a = 8; b = -66; c = -5;
Δ = b2-4ac
Δ = -662-4·8·(-5)
Δ = 4516
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:

$\sqrt{\Delta}=\sqrt{4516}=\sqrt{4*1129}=\sqrt{4}*\sqrt{1129}=2\sqrt{1129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1129}}{2*8}=\frac{66-2\sqrt{1129}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1129}}{2*8}=\frac{66+2\sqrt{1129}}{16}
$