756=450+0,5*x(x+1)

Solution for 756=450+0,5*x(x+1) equation:

756=450+0.5x(x+1)

We move all terms to the left:

756-(450+0.5x(x+1))=0


We calculate terms in parentheses: -(450+0.5x(x+1)), so:

450+0.5x(x+1)

determiningTheFunctionDomain
0.5x(x+1)+450

We multiply parentheses

0x^2+0x+450

We add all the numbers together, and all the variables

x^2+x+450

Back to the equation:

-(x^2+x+450)


We get rid of parentheses

-x^2-x-450+756=0

We add all the numbers together, and all the variables

-1x^2-1x+306=0

a = -1; b = -1; c = +306;
Δ = b2-4ac
Δ = -12-4·(-1)·306
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-35}{2*-1}=\frac{-34}{-2}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+35}{2*-1}=\frac{36}{-2}
=-18
$