x^2-4x-42=-7

Solution for x^2-4x-42=-7 equation:

x^2-4x-42=-7

We move all terms to the left:

x^2-4x-42-(-7)=0

We add all the numbers together, and all the variables

x^2-4x-35=0

a = 1; b = -4; c = -35;
Δ = b2-4ac
Δ = -42-4·1·(-35)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{39}}{2*1}=\frac{4-2\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{39}}{2*1}=\frac{4+2\sqrt{39}}{2}
$