3x+2/5x+4=0

Solution for 3x+2/5x+4=0 equation:

3x+2/5x+4=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

15x^2+20x+2=0

a = 15; b = 20; c = +2;
Δ = b2-4ac
Δ = 202-4·15·2
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{70}}{2*15}=\frac{-20-2\sqrt{70}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{70}}{2*15}=\frac{-20+2\sqrt{70}}{30}
$