x(x-35)+0.5x(x-64)=360

Solution for x(x-35)+0.5x(x-64)=360 equation:

x(x-35)+0.5x(x-64)=360

We move all terms to the left:

x(x-35)+0.5x(x-64)-(360)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2-34x-360=0

a = 2; b = -34; c = -360;
Δ = b2-4ac
Δ = -342-4·2·(-360)
Δ = 4036
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:

$\sqrt{\Delta}=\sqrt{4036}=\sqrt{4*1009}=\sqrt{4}*\sqrt{1009}=2\sqrt{1009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{1009}}{2*2}=\frac{34-2\sqrt{1009}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{1009}}{2*2}=\frac{34+2\sqrt{1009}}{4}
$