x2=97/84

Solution for x2=97/84 equation:

x2=97/84

We move all terms to the left:

x2-(97/84)=0

We add all the numbers together, and all the variables

x2-(+97/84)=0

We add all the numbers together, and all the variables

x^2-(+97/84)=0

We get rid of parentheses

x^2-97/84=0

We multiply all the terms by the denominator


x^2*84-97=0

Wy multiply elements

84x^2-97=0

a = 84; b = 0; c = -97;
Δ = b2-4ac
Δ = 02-4·84·(-97)
Δ = 32592
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:

$\sqrt{\Delta}=\sqrt{32592}=\sqrt{16*2037}=\sqrt{16}*\sqrt{2037}=4\sqrt{2037}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2037}}{2*84}=\frac{0-4\sqrt{2037}}{168}
=-\frac{4\sqrt{2037}}{168}
=-\frac{\sqrt{2037}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2037}}{2*84}=\frac{0+4\sqrt{2037}}{168}
=\frac{4\sqrt{2037}}{168}
=\frac{\sqrt{2037}}{42}
$