9x^2-69x-42=0

Solution for 9x^2-69x-42=0 equation:

9x^2-69x-42=0

a = 9; b = -69; c = -42;
Δ = b2-4ac
Δ = -692-4·9·(-42)
Δ = 6273
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:

$\sqrt{\Delta}=\sqrt{6273}=\sqrt{9*697}=\sqrt{9}*\sqrt{697}=3\sqrt{697}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-3\sqrt{697}}{2*9}=\frac{69-3\sqrt{697}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+3\sqrt{697}}{2*9}=\frac{69+3\sqrt{697}}{18}
$