5x+3/4x+8=0

Solution for 5x+3/4x+8=0 equation:

5x+3/4x+8=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


5x*4x+8*4x+3=0

Wy multiply elements

20x^2+32x+3=0

a = 20; b = 32; c = +3;
Δ = b2-4ac
Δ = 322-4·20·3
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-28}{2*20}=\frac{-60}{40}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+28}{2*20}=\frac{-4}{40}
=-1/10
$