X=(x+5)(x-4)

Solution for X=(x+5)(x-4) equation:

X=(X+5)(X-4)

We move all terms to the left:

X-((X+5)(X-4))=0

We multiply parentheses ..

-((+X^2-4X+5X-20))+X=0


We calculate terms in parentheses: -((+X^2-4X+5X-20)), so:

(+X^2-4X+5X-20)

We get rid of parentheses

X^2-4X+5X-20

We add all the numbers together, and all the variables

X^2+X-20

Back to the equation:

-(X^2+X-20)


We add all the numbers together, and all the variables

X-(X^2+X-20)=0

We get rid of parentheses

-X^2+X-X+20=0

We add all the numbers together, and all the variables

-1X^2+20=0

a = -1; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-1)·20
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*-1}=\frac{0-4\sqrt{5}}{-2}
=-\frac{4\sqrt{5}}{-2}
=-\frac{2\sqrt{5}}{-1}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*-1}=\frac{0+4\sqrt{5}}{-2}
=\frac{4\sqrt{5}}{-2}
=\frac{2\sqrt{5}}{-1}
$