112=4x(x+6)

Solution for 112=4x(x+6) equation:

112=4x(x+6)

We move all terms to the left:

112-(4x(x+6))=0


We calculate terms in parentheses: -(4x(x+6)), so:

4x(x+6)

We multiply parentheses

4x^2+24x

Back to the equation:

-(4x^2+24x)


We get rid of parentheses

-4x^2-24x+112=0

a = -4; b = -24; c = +112;
Δ = b2-4ac
Δ = -242-4·(-4)·112
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{37}}{2*-4}=\frac{24-8\sqrt{37}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{37}}{2*-4}=\frac{24+8\sqrt{37}}{-8}
$