-10x(x+4)+42=-19-19

Solution for -10x(x+4)+42=-19-19 equation:

-10x(x+4)+42=-19-19

We move all terms to the left:

-10x(x+4)+42-(-19-19)=0

We add all the numbers together, and all the variables

-10x(x+4)+42-(-38)=0

We add all the numbers together, and all the variables

-10x(x+4)+80=0

We multiply parentheses

-10x^2-40x+80=0

a = -10; b = -40; c = +80;
Δ = b2-4ac
Δ = -402-4·(-10)·80
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{3}}{2*-10}=\frac{40-40\sqrt{3}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{3}}{2*-10}=\frac{40+40\sqrt{3}}{-20}
$