465x=x^2+6750

Solution for 465x=x^2+6750 equation:

465x=x^2+6750

We move all terms to the left:

465x-(x^2+6750)=0

We get rid of parentheses

-x^2+465x-6750=0

We add all the numbers together, and all the variables

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