13^2=5x(5x+9)

Solution for 13^2=5x(5x+9) equation:

13^2=5x(5x+9)

We move all terms to the left:

13^2-(5x(5x+9))=0

We add all the numbers together, and all the variables

-(5x(5x+9))+169=0


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

5x(5x+9)

We multiply parentheses

25x^2+45x

Back to the equation:

-(25x^2+45x)


We get rid of parentheses

-25x^2-45x+169=0

a = -25; b = -45; c = +169;
Δ = b2-4ac
Δ = -452-4·(-25)·169
Δ = 18925
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:

$\sqrt{\Delta}=\sqrt{18925}=\sqrt{25*757}=\sqrt{25}*\sqrt{757}=5\sqrt{757}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5\sqrt{757}}{2*-25}=\frac{45-5\sqrt{757}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5\sqrt{757}}{2*-25}=\frac{45+5\sqrt{757}}{-50}
$