360=1/2x+x(x-35)+(x-46)

Solution for 360=1/2x+x(x-35)+(x-46) equation:

360=1/2x+x(x-35)+(x-46)

We move all terms to the left:

360-(1/2x+x(x-35)+(x-46))=0


Domain of the equation: 2x+x(x-35)+(x-46))!=0

x∈R


We multiply all the terms by the denominator


-(1+360*2x+x(x-35)+(x-46))=0


We calculate terms in parentheses: -(1+360*2x+x(x-35)+(x-46)), so:

1+360*2x+x(x-35)+(x-46)

determiningTheFunctionDomain
360*2x+x(x-35)+(x-46)+1

We multiply parentheses

x^2+360*2x-35x+(x-46)+1

Wy multiply elements

x^2+720x-35x+(x-46)+1

We get rid of parentheses

x^2+720x-35x+x-46+1

We add all the numbers together, and all the variables

x^2+686x-45

Back to the equation:

-(x^2+686x-45)


We get rid of parentheses

-x^2-686x+45=0

We add all the numbers together, and all the variables

-1x^2-686x+45=0

a = -1; b = -686; c = +45;
Δ = b2-4ac
Δ = -6862-4·(-1)·45
Δ = 470776
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:

$\sqrt{\Delta}=\sqrt{470776}=\sqrt{4*117694}=\sqrt{4}*\sqrt{117694}=2\sqrt{117694}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-686)-2\sqrt{117694}}{2*-1}=\frac{686-2\sqrt{117694}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-686)+2\sqrt{117694}}{2*-1}=\frac{686+2\sqrt{117694}}{-2}
$