x^2=110/361

Solution for x^2=110/361 equation:

x^2=110/361

We move all terms to the left:

x^2-(110/361)=0

We add all the numbers together, and all the variables

x^2-(+110/361)=0

We get rid of parentheses

x^2-110/361=0

We multiply all the terms by the denominator


x^2*361-110=0

Wy multiply elements

361x^2-110=0

a = 361; b = 0; c = -110;
Δ = b2-4ac
Δ = 02-4·361·(-110)
Δ = 158840
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:

$\sqrt{\Delta}=\sqrt{158840}=\sqrt{1444*110}=\sqrt{1444}*\sqrt{110}=38\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-38\sqrt{110}}{2*361}=\frac{0-38\sqrt{110}}{722}
=-\frac{38\sqrt{110}}{722}
=-\frac{\sqrt{110}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+38\sqrt{110}}{2*361}=\frac{0+38\sqrt{110}}{722}
=\frac{38\sqrt{110}}{722}
=\frac{\sqrt{110}}{19}
$