X=(15-2x)(20-x)

Solution for X=(15-2x)(20-x) equation:

X=(15-2X)(20-X)

We move all terms to the left:

X-((15-2X)(20-X))=0

We add all the numbers together, and all the variables

X-((-2X+15)(-1X+20))=0

We multiply parentheses ..

-((+2X^2-40X-15X+300))+X=0


We calculate terms in parentheses: -((+2X^2-40X-15X+300)), so:

(+2X^2-40X-15X+300)

We get rid of parentheses

2X^2-40X-15X+300

We add all the numbers together, and all the variables

2X^2-55X+300

Back to the equation:

-(2X^2-55X+300)


We add all the numbers together, and all the variables

X-(2X^2-55X+300)=0

We get rid of parentheses

-2X^2+X+55X-300=0

We add all the numbers together, and all the variables

-2X^2+56X-300=0

a = -2; b = 56; c = -300;
Δ = b2-4ac
Δ = 562-4·(-2)·(-300)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{46}}{2*-2}=\frac{-56-4\sqrt{46}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{46}}{2*-2}=\frac{-56+4\sqrt{46}}{-4}
$