X2+13x+42=9

Solution for X2+13x+42=9 equation:

X2+13X+42=9

We move all terms to the left:

X2+13X+42-(9)=0

We add all the numbers together, and all the variables

X^2+13X+33=0

a = 1; b = 13; c = +33;
Δ = b2-4ac
Δ = 132-4·1·33
Δ = 37
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{37}}{2*1}=\frac{-13-\sqrt{37}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{37}}{2*1}=\frac{-13+\sqrt{37}}{2}
$