x^2=(25)/(89)

Solution for x^2=(25)/(89) equation:

x^2=(25)/(89)

We move all terms to the left:

x^2-((25)/(89))=0

We add all the numbers together, and all the variables

x^2-(+25/89)=0

We get rid of parentheses

x^2-25/89=0

We multiply all the terms by the denominator


x^2*89-25=0

Wy multiply elements

89x^2-25=0

a = 89; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·89·(-25)
Δ = 8900
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:

$\sqrt{\Delta}=\sqrt{8900}=\sqrt{100*89}=\sqrt{100}*\sqrt{89}=10\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{89}}{2*89}=\frac{0-10\sqrt{89}}{178}
=-\frac{10\sqrt{89}}{178}
=-\frac{5\sqrt{89}}{89}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{89}}{2*89}=\frac{0+10\sqrt{89}}{178}
=\frac{10\sqrt{89}}{178}
=\frac{5\sqrt{89}}{89}
$