9x^2/5=36

Solution for 9x^2/5=36 equation:

9x^2/5=36

We move all terms to the left:

9x^2/5-(36)=0

We multiply all the terms by the denominator


9x^2-36*5=0

We add all the numbers together, and all the variables

9x^2-180=0

a = 9; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·9·(-180)
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{5}}{2*9}=\frac{0-36\sqrt{5}}{18}
=-\frac{36\sqrt{5}}{18}
=-2\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{5}}{2*9}=\frac{0+36\sqrt{5}}{18}
=\frac{36\sqrt{5}}{18}
=2\sqrt{5}
$