x2=14/9

Solution for x2=14/9 equation:

x2=14/9

We move all terms to the left:

x2-(14/9)=0

We add all the numbers together, and all the variables

x2-(+14/9)=0

We add all the numbers together, and all the variables

x^2-(+14/9)=0

We get rid of parentheses

x^2-14/9=0

We multiply all the terms by the denominator


x^2*9-14=0

Wy multiply elements

9x^2-14=0

a = 9; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·9·(-14)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{14}}{2*9}=\frac{0-6\sqrt{14}}{18}
=-\frac{6\sqrt{14}}{18}
=-\frac{\sqrt{14}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{14}}{2*9}=\frac{0+6\sqrt{14}}{18}
=\frac{6\sqrt{14}}{18}
=\frac{\sqrt{14}}{3}
$