x2+42x-9=0

Solution for x2+42x-9=0 equation:

x2+42x-9=0

We add all the numbers together, and all the variables

x^2+42x-9=0

a = 1; b = 42; c = -9;
Δ = b2-4ac
Δ = 422-4·1·(-9)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30\sqrt{2}}{2*1}=\frac{-42-30\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30\sqrt{2}}{2*1}=\frac{-42+30\sqrt{2}}{2}
$