X+18=4x(x-48)

Solution for X+18=4x(x-48) equation:

X+18=4X(X-48)

We move all terms to the left:

X+18-(4X(X-48))=0


We calculate terms in parentheses: -(4X(X-48)), so:

4X(X-48)

We multiply parentheses

4X^2-192X

Back to the equation:

-(4X^2-192X)


We get rid of parentheses

-4X^2+X+192X+18=0

We add all the numbers together, and all the variables

-4X^2+193X+18=0

a = -4; b = 193; c = +18;
Δ = b2-4ac
Δ = 1932-4·(-4)·18
Δ = 37537
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{-(193)-\sqrt{37537}}{2*-4}=\frac{-193-\sqrt{37537}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(193)+\sqrt{37537}}{2*-4}=\frac{-193+\sqrt{37537}}{-8}
$