3x^2/4+8x+20=0

Solution for 3x^2/4+8x+20=0 equation:

3x^2/4+8x+20=0

We multiply all the terms by the denominator


3x^2+8x*4+20*4=0

We add all the numbers together, and all the variables

3x^2+8x*4+80=0

Wy multiply elements

3x^2+32x+80=0

a = 3; b = 32; c = +80;
Δ = b2-4ac
Δ = 322-4·3·80
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{-(32)-8}{2*3}=\frac{-40}{6}
=-6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8}{2*3}=\frac{-24}{6}
=-4
$