x^2-(39/4)x+(165/4)=0

Solution for x^2-(39/4)x+(165/4)=0 equation:

x^2-(39/4)x+(165/4)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x^2-(+39/4)x+(+165/4)=0

We multiply parentheses

x^2-39x^2+(+165/4)=0

We get rid of parentheses

x^2-39x^2+165/4=0

We multiply all the terms by the denominator


x^2*4-39x^2*4+165=0

Wy multiply elements

4x^2-156x^2+165=0

We add all the numbers together, and all the variables

-152x^2+165=0

a = -152; b = 0; c = +165;
Δ = b2-4ac
Δ = 02-4·(-152)·165
Δ = 100320
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:

$\sqrt{\Delta}=\sqrt{100320}=\sqrt{16*6270}=\sqrt{16}*\sqrt{6270}=4\sqrt{6270}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6270}}{2*-152}=\frac{0-4\sqrt{6270}}{-304}
=-\frac{4\sqrt{6270}}{-304}
=-\frac{\sqrt{6270}}{-76}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6270}}{2*-152}=\frac{0+4\sqrt{6270}}{-304}
=\frac{4\sqrt{6270}}{-304}
=\frac{\sqrt{6270}}{-76}
$