2025=x(x+40)

Solution for 2025=x(x+40) equation:

2025=x(x+40)

We move all terms to the left:

2025-(x(x+40))=0


We calculate terms in parentheses: -(x(x+40)), so:

x(x+40)

We multiply parentheses

x^2+40x

Back to the equation:

-(x^2+40x)


We get rid of parentheses

-x^2-40x+2025=0

We add all the numbers together, and all the variables

-1x^2-40x+2025=0

a = -1; b = -40; c = +2025;
Δ = b2-4ac
Δ = -402-4·(-1)·2025
Δ = 9700
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:

$\sqrt{\Delta}=\sqrt{9700}=\sqrt{100*97}=\sqrt{100}*\sqrt{97}=10\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{97}}{2*-1}=\frac{40-10\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{97}}{2*-1}=\frac{40+10\sqrt{97}}{-2}
$