x(x+4)=80/3

Solution for x(x+4)=80/3 equation:

x(x+4)=80/3

We move all terms to the left:

x(x+4)-(80/3)=0

We add all the numbers together, and all the variables

x(x+4)-(+80/3)=0

We multiply parentheses

x^2+4x-(+80/3)=0

We get rid of parentheses

x^2+4x-80/3=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+12x-80=0

a = 3; b = 12; c = -80;
Δ = b2-4ac
Δ = 122-4·3·(-80)
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{69}}{2*3}=\frac{-12-4\sqrt{69}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{69}}{2*3}=\frac{-12+4\sqrt{69}}{6}
$