337=6x(15-x)

Solution for 337=6x(15-x) equation:

337=6x(15-x)

We move all terms to the left:

337-(6x(15-x))=0

We add all the numbers together, and all the variables

-(6x(-1x+15))+337=0


We calculate terms in parentheses: -(6x(-1x+15)), so:

6x(-1x+15)

We multiply parentheses

-6x^2+90x

Back to the equation:

-(-6x^2+90x)


We get rid of parentheses

6x^2-90x+337=0

a = 6; b = -90; c = +337;
Δ = b2-4ac
Δ = -902-4·6·337
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{3}}{2*6}=\frac{90-2\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{3}}{2*6}=\frac{90+2\sqrt{3}}{12}
$