-4x(x+6)=-9x-19

Solution for -4x(x+6)=-9x-19 equation:

-4x(x+6)=-9x-19

We move all terms to the left:

-4x(x+6)-(-9x-19)=0

We multiply parentheses

-4x^2-24x-(-9x-19)=0

We get rid of parentheses

-4x^2-24x+9x+19=0

We add all the numbers together, and all the variables

-4x^2-15x+19=0

a = -4; b = -15; c = +19;
Δ = b2-4ac
Δ = -152-4·(-4)·19
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-23}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+23}{2*-4}=\frac{38}{-8}
=-4+3/4
$