169x^2-169x=-4

Solution for 169x^2-169x=-4 equation:

169x^2-169x=-4

We move all terms to the left:

169x^2-169x-(-4)=0

We add all the numbers together, and all the variables

169x^2-169x+4=0

a = 169; b = -169; c = +4;
Δ = b2-4ac
Δ = -1692-4·169·4
Δ = 25857
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:

$\sqrt{\Delta}=\sqrt{25857}=\sqrt{1521*17}=\sqrt{1521}*\sqrt{17}=39\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-169)-39\sqrt{17}}{2*169}=\frac{169-39\sqrt{17}}{338}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-169)+39\sqrt{17}}{2*169}=\frac{169+39\sqrt{17}}{338}
$