6750=-x(x-465)

Solution for 6750=-x(x-465) equation:

6750=-x(x-465)

We move all terms to the left:

6750-(-x(x-465))=0


We calculate terms in parentheses: -(-x(x-465)), so:

-x(x-465)

We multiply parentheses

-x^2+465x

We add all the numbers together, and all the variables

-1x^2+465x

Back to the equation:

-(-1x^2+465x)


We get rid of parentheses

1x^2-465x+6750=0

We add all the numbers together, and all the variables

x^2-465x+6750=0

a = 1; b = -465; c = +6750;
Δ = b2-4ac
Δ = -4652-4·1·6750
Δ = 189225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{189225}=435$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-465)-435}{2*1}=\frac{30}{2}
=15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-465)+435}{2*1}=\frac{900}{2}
=450
$