(13x-5)(13x-5)=90

Solution for (13x-5)(13x-5)=90 equation:

(13x-5)(13x-5)=90

We move all terms to the left:

(13x-5)(13x-5)-(90)=0

We multiply parentheses ..

(+169x^2-65x-65x+25)-90=0

We get rid of parentheses

169x^2-65x-65x+25-90=0

We add all the numbers together, and all the variables

169x^2-130x-65=0

a = 169; b = -130; c = -65;
Δ = b2-4ac
Δ = -1302-4·169·(-65)
Δ = 60840
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:

$\sqrt{\Delta}=\sqrt{60840}=\sqrt{6084*10}=\sqrt{6084}*\sqrt{10}=78\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-78\sqrt{10}}{2*169}=\frac{130-78\sqrt{10}}{338}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+78\sqrt{10}}{2*169}=\frac{130+78\sqrt{10}}{338}
$