6x^2=29.80(17-x)

Solution for 6x^2=29.80(17-x) equation:

6x^2=29.80(17-x)

We move all terms to the left:

6x^2-(29.80(17-x))=0

We add all the numbers together, and all the variables

6x^2-(29.80(-1x+17))=0


We calculate terms in parentheses: -(29.80(-1x+17)), so:

29.80(-1x+17)

We multiply parentheses

-29.8x+506.6

Back to the equation:

-(-29.8x+506.6)


We get rid of parentheses

6x^2+29.8x-506.6=0

a = 6; b = 29.8; c = -506.6;
Δ = b2-4ac
Δ = 29.82-4·6·(-506.6)
Δ = 13046.44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29.8)-\sqrt{13046.44}}{2*6}=\frac{-29.8-\sqrt{13046.44}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29.8)+\sqrt{13046.44}}{2*6}=\frac{-29.8+\sqrt{13046.44}}{12}
$