X(x+4)-3=4x+19.5

Solution for X(x+4)-3=4x+19.5 equation:

X(X+4)-3=4X+19.5

We move all terms to the left:

X(X+4)-3-(4X+19.5)=0

We multiply parentheses

X^2+4X-(4X+19.5)-3=0

We get rid of parentheses

X^2+4X-4X-19.5-3=0

We add all the numbers together, and all the variables

X^2-22.5=0

a = 1; b = 0; c = -22.5;
Δ = b2-4ac
Δ = 02-4·1·(-22.5)
Δ = 90
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:

$\sqrt{\Delta}=\sqrt{90}=\sqrt{9*10}=\sqrt{9}*\sqrt{10}=3\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{10}}{2*1}=\frac{0-3\sqrt{10}}{2}
=-\frac{3\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{10}}{2*1}=\frac{0+3\sqrt{10}}{2}
=\frac{3\sqrt{10}}{2}
$