9x^2-21x-5=3

Solution for 9x^2-21x-5=3 equation:

9x^2-21x-5=3

We move all terms to the left:

9x^2-21x-5-(3)=0

We add all the numbers together, and all the variables

9x^2-21x-8=0

a = 9; b = -21; c = -8;
Δ = b2-4ac
Δ = -212-4·9·(-8)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-27}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+27}{2*9}=\frac{48}{18}
=2+2/3
$