2x+3=-3/4x

Solution for 2x+3=-3/4x equation:

2x+3=-3/4x

We move all terms to the left:

2x+3-(-3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

2x+3/4x+3=0

We multiply all the terms by the denominator


2x*4x+3*4x+3=0

Wy multiply elements

8x^2+12x+3=0

a = 8; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·8·3
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{3}}{2*8}=\frac{-12-4\sqrt{3}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{3}}{2*8}=\frac{-12+4\sqrt{3}}{16}
$