x^2-(220x/6)-412575=0

Solution for x^2-(220x/6)-412575=0 equation:

x^2-(220x/6)-412575=0

We add all the numbers together, and all the variables

x^2-(+220x/6)-412575=0

We get rid of parentheses

x^2-220x/6-412575=0

We multiply all the terms by the denominator


x^2*6-220x-412575*6=0

We add all the numbers together, and all the variables

x^2*6-220x-2475450=0

Wy multiply elements

6x^2-220x-2475450=0

a = 6; b = -220; c = -2475450;
Δ = b2-4ac
Δ = -2202-4·6·(-2475450)
Δ = 59459200
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:

$\sqrt{\Delta}=\sqrt{59459200}=\sqrt{1600*37162}=\sqrt{1600}*\sqrt{37162}=40\sqrt{37162}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-40\sqrt{37162}}{2*6}=\frac{220-40\sqrt{37162}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+40\sqrt{37162}}{2*6}=\frac{220+40\sqrt{37162}}{12}
$