6x^2=2.80(17-x)

Solution for 6x^2=2.80(17-x) equation:

6x^2=2.80(17-x)

We move all terms to the left:

6x^2-(2.80(17-x))=0

We add all the numbers together, and all the variables

6x^2-(2.80(-1x+17))=0


We calculate terms in parentheses: -(2.80(-1x+17)), so:

2.80(-1x+17)

We multiply parentheses

-2.8x+47.6

Back to the equation:

-(-2.8x+47.6)


We get rid of parentheses

6x^2+2.8x-47.6=0

a = 6; b = 2.8; c = -47.6;
Δ = b2-4ac
Δ = 2.82-4·6·(-47.6)
Δ = 1150.24
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{-(2.8)-\sqrt{1150.24}}{2*6}=\frac{-2.8-\sqrt{1150.24}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.8)+\sqrt{1150.24}}{2*6}=\frac{-2.8+\sqrt{1150.24}}{12}
$