4x(x-12)+19=-89

Solution for 4x(x-12)+19=-89 equation:

4x(x-12)+19=-89

We move all terms to the left:

4x(x-12)+19-(-89)=0

We add all the numbers together, and all the variables

4x(x-12)+108=0

We multiply parentheses

4x^2-48x+108=0

a = 4; b = -48; c = +108;
Δ = b2-4ac
Δ = -482-4·4·108
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24}{2*4}=\frac{24}{8}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24}{2*4}=\frac{72}{8}
=9
$