x^2-7x-7*42=0

Solution for x^2-7x-7*42=0 equation:

x^2-7x-7*42=0

We add all the numbers together, and all the variables

x^2-7x-294=0

a = 1; b = -7; c = -294;
Δ = b2-4ac
Δ = -72-4·1·(-294)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-35}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+35}{2*1}=\frac{42}{2}
=21
$