2.5x(x-10)+(x-40)+x=360

Solution for 2.5x(x-10)+(x-40)+x=360 equation:

2.5x(x-10)+(x-40)+x=360

We move all terms to the left:

2.5x(x-10)+(x-40)+x-(360)=0

We add all the numbers together, and all the variables

x+2.5x(x-10)+(x-40)-360=0

We multiply parentheses

2x^2+x-20x+(x-40)-360=0

We get rid of parentheses

2x^2+x-20x+x-40-360=0

We add all the numbers together, and all the variables

2x^2-18x-400=0

a = 2; b = -18; c = -400;
Δ = b2-4ac
Δ = -182-4·2·(-400)
Δ = 3524
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:

$\sqrt{\Delta}=\sqrt{3524}=\sqrt{4*881}=\sqrt{4}*\sqrt{881}=2\sqrt{881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{881}}{2*2}=\frac{18-2\sqrt{881}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{881}}{2*2}=\frac{18+2\sqrt{881}}{4}
$