x^2-13x+42=9900

Solution for x^2-13x+42=9900 equation:

x^2-13x+42=9900

We move all terms to the left:

x^2-13x+42-(9900)=0

We add all the numbers together, and all the variables

x^2-13x-9858=0

a = 1; b = -13; c = -9858;
Δ = b2-4ac
Δ = -132-4·1·(-9858)
Δ = 39601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39601}=199$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-199}{2*1}=\frac{-186}{2}
=-93
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+199}{2*1}=\frac{212}{2}
=106
$