X(30+8x)=334

Solution for X(30+8x)=334 equation:

X(30+8X)=334

We move all terms to the left:

X(30+8X)-(334)=0

We add all the numbers together, and all the variables

X(8X+30)-334=0

We multiply parentheses

8X^2+30X-334=0

a = 8; b = 30; c = -334;
Δ = b2-4ac
Δ = 302-4·8·(-334)
Δ = 11588
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:

$\sqrt{\Delta}=\sqrt{11588}=\sqrt{4*2897}=\sqrt{4}*\sqrt{2897}=2\sqrt{2897}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{2897}}{2*8}=\frac{-30-2\sqrt{2897}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{2897}}{2*8}=\frac{-30+2\sqrt{2897}}{16}
$