4x=5/2x-4

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

4x=5/2x-4

We move all terms to the left:

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


Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

4x-5/2x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2+8x-5=0

a = 8; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·8·(-5)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{14}}{2*8}=\frac{-8-4\sqrt{14}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{14}}{2*8}=\frac{-8+4\sqrt{14}}{16}
$