8x^2-21x=9

Solution for 8x^2-21x=9 equation:

8x^2-21x=9

We move all terms to the left:

8x^2-21x-(9)=0

a = 8; b = -21; c = -9;
Δ = b2-4ac
Δ = -212-4·8·(-9)
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*8}=\frac{-6}{16}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+27}{2*8}=\frac{48}{16}
=3
$