2x+5=-3/4x

Solution for 2x+5=-3/4x equation:

2x+5=-3/4x

We move all terms to the left:

2x+5-(-3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

2x+3/4x+5=0

We multiply all the terms by the denominator


2x*4x+5*4x+3=0

Wy multiply elements

8x^2+20x+3=0

a = 8; b = 20; c = +3;
Δ = b2-4ac
Δ = 202-4·8·3
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{19}}{2*8}=\frac{-20-4\sqrt{19}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{19}}{2*8}=\frac{-20+4\sqrt{19}}{16}
$