2.4x(x+20)=-6

Solution for 2.4x(x+20)=-6 equation:

2.4x(x+20)=-6

We move all terms to the left:

2.4x(x+20)-(-6)=0

We add all the numbers together, and all the variables

2.4x(x+20)+6=0

We multiply parentheses

2x^2+40x+6=0

a = 2; b = 40; c = +6;
Δ = b2-4ac
Δ = 402-4·2·6
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{97}}{2*2}=\frac{-40-4\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{97}}{2*2}=\frac{-40+4\sqrt{97}}{4}
$