(x+4)(3x)=(8)(8+19)

Solution for (x+4)(3x)=(8)(8+19) equation:

(x+4)(3x)=(8)(8+19)

We move all terms to the left:

(x+4)(3x)-((8)(8+19))=0

We add all the numbers together, and all the variables

(x+4)3x-(827)=0

We add all the numbers together, and all the variables

(x+4)3x-827=0

We multiply parentheses

3x^2+12x-827=0

a = 3; b = 12; c = -827;
Δ = b2-4ac
Δ = 122-4·3·(-827)
Δ = 10068
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:

$\sqrt{\Delta}=\sqrt{10068}=\sqrt{4*2517}=\sqrt{4}*\sqrt{2517}=2\sqrt{2517}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{2517}}{2*3}=\frac{-12-2\sqrt{2517}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{2517}}{2*3}=\frac{-12+2\sqrt{2517}}{6}
$