-x(2x+14)=5x+2

Solution for -x(2x+14)=5x+2 equation:

-x(2x+14)=5x+2

We move all terms to the left:

-x(2x+14)-(5x+2)=0

We multiply parentheses

-2x^2-14x-(5x+2)=0

We get rid of parentheses

-2x^2-14x-5x-2=0

We add all the numbers together, and all the variables

-2x^2-19x-2=0

a = -2; b = -19; c = -2;
Δ = b2-4ac
Δ = -192-4·(-2)·(-2)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{345}}{2*-2}=\frac{19-\sqrt{345}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{345}}{2*-2}=\frac{19+\sqrt{345}}{-4}
$