5=9x(9x-5)

Solution for 5=9x(9x-5) equation:

5=9x(9x-5)

We move all terms to the left:

5-(9x(9x-5))=0


We calculate terms in parentheses: -(9x(9x-5)), so:

9x(9x-5)

We multiply parentheses

81x^2-45x

Back to the equation:

-(81x^2-45x)


We get rid of parentheses

-81x^2+45x+5=0

a = -81; b = 45; c = +5;
Δ = b2-4ac
Δ = 452-4·(-81)·5
Δ = 3645
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:

$\sqrt{\Delta}=\sqrt{3645}=\sqrt{729*5}=\sqrt{729}*\sqrt{5}=27\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-27\sqrt{5}}{2*-81}=\frac{-45-27\sqrt{5}}{-162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+27\sqrt{5}}{2*-81}=\frac{-45+27\sqrt{5}}{-162}
$