10,5=(60*x*(36-x))/36^2

Solution for 10,5=(60*x*(36-x))/36^2 equation:

10.5=(60x(36-x))/36^2

We move all terms to the left:

10.5-((60x(36-x))/36^2)=0

We add all the numbers together, and all the variables

-((60x(-1x+36))/36^2)+10.5=0

We multiply all the terms by the denominator


-((60x(-1x+36))+(10.5)*36^2)=0


We calculate terms in parentheses: -((60x(-1x+36))+(10.5)*36^2), so:

(60x(-1x+36))+(10.5)*36^2

We add all the numbers together, and all the variables

(60x(-1x+36))+13608


We calculate terms in parentheses: +(60x(-1x+36)), so:

60x(-1x+36)

We multiply parentheses

-60x^2+2160x

Back to the equation:

+(-60x^2+2160x)


We get rid of parentheses

-60x^2+2160x+13608

Back to the equation:

-(-60x^2+2160x+13608)


We get rid of parentheses

60x^2-2160x-13608=0

a = 60; b = -2160; c = -13608;
Δ = b2-4ac
Δ = -21602-4·60·(-13608)
Δ = 7931520
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:

$\sqrt{\Delta}=\sqrt{7931520}=\sqrt{46656*170}=\sqrt{46656}*\sqrt{170}=216\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2160)-216\sqrt{170}}{2*60}=\frac{2160-216\sqrt{170}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2160)+216\sqrt{170}}{2*60}=\frac{2160+216\sqrt{170}}{120}
$