x2=13x+42

Solution for x2=13x+42 equation:

x2=13x+42

We move all terms to the left:

x2-(13x+42)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2-13x-42=0

a = 1; b = -13; c = -42;
Δ = b2-4ac
Δ = -132-4·1·(-42)
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{337}}{2*1}=\frac{13-\sqrt{337}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{337}}{2*1}=\frac{13+\sqrt{337}}{2}
$