7x^2-6x-21=-5

Solution for 7x^2-6x-21=-5 equation:

7x^2-6x-21=-5

We move all terms to the left:

7x^2-6x-21-(-5)=0

We add all the numbers together, and all the variables

7x^2-6x-16=0

a = 7; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·7·(-16)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-22}{2*7}=\frac{-16}{14}
=-1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+22}{2*7}=\frac{28}{14}
=2
$