34/9=x2

Solution for 34/9=x2 equation:

34/9=x2

We move all terms to the left:

34/9-(x2)=0

We add all the numbers together, and all the variables

-1x^2+34/9=0

We multiply all the terms by the denominator


-1x^2*9+34=0

Wy multiply elements

-9x^2+34=0

a = -9; b = 0; c = +34;
Δ = b2-4ac
Δ = 02-4·(-9)·34
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{34}}{2*-9}=\frac{0-6\sqrt{34}}{-18}
=-\frac{6\sqrt{34}}{-18}
=-\frac{\sqrt{34}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{34}}{2*-9}=\frac{0+6\sqrt{34}}{-18}
=\frac{6\sqrt{34}}{-18}
=\frac{\sqrt{34}}{-3}
$