-7x^2-42x=27

Solution for -7x^2-42x=27 equation:

-7x^2-42x=27

We move all terms to the left:

-7x^2-42x-(27)=0

a = -7; b = -42; c = -27;
Δ = b2-4ac
Δ = -422-4·(-7)·(-27)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-12\sqrt{7}}{2*-7}=\frac{42-12\sqrt{7}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+12\sqrt{7}}{2*-7}=\frac{42+12\sqrt{7}}{-14}
$