16=6(x-5)4x

Solution for 16=6(x-5)4x equation:

16=6(x-5)4x

We move all terms to the left:

16-(6(x-5)4x)=0


We calculate terms in parentheses: -(6(x-5)4x), so:

6(x-5)4x

We multiply parentheses

24x^2-120x

Back to the equation:

-(24x^2-120x)


We get rid of parentheses

-24x^2+120x+16=0

a = -24; b = 120; c = +16;
Δ = b2-4ac
Δ = 1202-4·(-24)·16
Δ = 15936
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:

$\sqrt{\Delta}=\sqrt{15936}=\sqrt{64*249}=\sqrt{64}*\sqrt{249}=8\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-8\sqrt{249}}{2*-24}=\frac{-120-8\sqrt{249}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+8\sqrt{249}}{2*-24}=\frac{-120+8\sqrt{249}}{-48}
$