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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We multiply parentheses

x^2+x*2x-46x-35*2x-360*2x=0

Wy multiply elements

x^2+2x^2-46x-70x-720x=0

We add all the numbers together, and all the variables

3x^2-836x=0

a = 3; b = -836; c = 0;
Δ = b2-4ac
Δ = -8362-4·3·0
Δ = 698896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{698896}=836$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-836)-836}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-836)+836}{2*3}=\frac{1672}{6}
=278+2/3
$