294=x(6x+x)

Solution for 294=x(6x+x) equation:

294=x(6x+x)

We move all terms to the left:

294-(x(6x+x))=0

We add all the numbers together, and all the variables

-(x(+7x))+294=0


We calculate terms in parentheses: -(x(+7x)), so:

x(+7x)

We multiply parentheses

7x^2

Back to the equation:

-(7x^2)


a = -7; b = 0; c = +294;
Δ = b2-4ac
Δ = 02-4·(-7)·294
Δ = 8232
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:

$\sqrt{\Delta}=\sqrt{8232}=\sqrt{196*42}=\sqrt{196}*\sqrt{42}=14\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{42}}{2*-7}=\frac{0-14\sqrt{42}}{-14}
=-\frac{14\sqrt{42}}{-14}
=-\frac{\sqrt{42}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{42}}{2*-7}=\frac{0+14\sqrt{42}}{-14}
=\frac{14\sqrt{42}}{-14}
=\frac{\sqrt{42}}{-1}
$