6x^2=31.4(16-x)

Solution for 6x^2=31.4(16-x) equation:

6x^2=31.4(16-x)

We move all terms to the left:

6x^2-(31.4(16-x))=0

We add all the numbers together, and all the variables

6x^2-(31.4(-1x+16))=0


We calculate terms in parentheses: -(31.4(-1x+16)), so:

31.4(-1x+16)

We multiply parentheses

-31.4x+502.4

Back to the equation:

-(-31.4x+502.4)


We get rid of parentheses

6x^2+31.4x-502.4=0

a = 6; b = 31.4; c = -502.4;
Δ = b2-4ac
Δ = 31.42-4·6·(-502.4)
Δ = 13043.56
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{-(31.4)-\sqrt{13043.56}}{2*6}=\frac{-31.4-\sqrt{13043.56}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31.4)+\sqrt{13043.56}}{2*6}=\frac{-31.4+\sqrt{13043.56}}{12}
$