4,9x-(x^2)/6-10=0

Solution for 4,9x-(x^2)/6-10=0 equation:

4.9x-(x^2)/6-10=0

determiningTheFunctionDomain
-x^2/6+4.9x-10=0

We multiply all the terms by the denominator


-x^2+(4.9x)*6-10*6=0

We add all the numbers together, and all the variables

-x^2+(+4.9x)*6-10*6=0

We add all the numbers together, and all the variables

-1x^2+(+4.9x)*6-60=0

We multiply parentheses

-1x^2+24x-60=0

a = -1; b = 24; c = -60;
Δ = b2-4ac
Δ = 242-4·(-1)·(-60)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{21}}{2*-1}=\frac{-24-4\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{21}}{2*-1}=\frac{-24+4\sqrt{21}}{-2}
$