4x+(2x(110-x))=360

Solution for 4x+(2x(110-x))=360 equation:

4x+(2x(110-x))=360

We move all terms to the left:

4x+(2x(110-x))-(360)=0

We add all the numbers together, and all the variables

4x+(2x(-1x+110))-360=0


We calculate terms in parentheses: +(2x(-1x+110)), so:

2x(-1x+110)

We multiply parentheses

-2x^2+220x

Back to the equation:

+(-2x^2+220x)


We get rid of parentheses

-2x^2+220x+4x-360=0

We add all the numbers together, and all the variables

-2x^2+224x-360=0

a = -2; b = 224; c = -360;
Δ = b2-4ac
Δ = 2242-4·(-2)·(-360)
Δ = 47296
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:

$\sqrt{\Delta}=\sqrt{47296}=\sqrt{64*739}=\sqrt{64}*\sqrt{739}=8\sqrt{739}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(224)-8\sqrt{739}}{2*-2}=\frac{-224-8\sqrt{739}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(224)+8\sqrt{739}}{2*-2}=\frac{-224+8\sqrt{739}}{-4}
$