8x(x-4)=9

Solution for 8x(x-4)=9 equation:

8x(x-4)=9

We move all terms to the left:

8x(x-4)-(9)=0

We multiply parentheses

8x^2-32x-9=0

a = 8; b = -32; c = -9;
Δ = b2-4ac
Δ = -322-4·8·(-9)
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{82}}{2*8}=\frac{32-4\sqrt{82}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{82}}{2*8}=\frac{32+4\sqrt{82}}{16}
$