3x+7/4x+5=0

Solution for 3x+7/4x+5=0 equation:

3x+7/4x+5=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


3x*4x+5*4x+7=0

Wy multiply elements

12x^2+20x+7=0

a = 12; b = 20; c = +7;
Δ = b2-4ac
Δ = 202-4·12·7
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8}{2*12}=\frac{-28}{24}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8}{2*12}=\frac{-12}{24}
=-1/2
$