2x=5/4x+6

Solution for 2x=5/4x+6 equation:

2x=5/4x+6

We move all terms to the left:

2x-(5/4x+6)=0


Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

2x-5/4x-6=0

We multiply all the terms by the denominator


2x*4x-6*4x-5=0

Wy multiply elements

8x^2-24x-5=0

a = 8; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·8·(-5)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{46}}{2*8}=\frac{24-4\sqrt{46}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{46}}{2*8}=\frac{24+4\sqrt{46}}{16}
$