8x(2x-9)=-3

Solution for 8x(2x-9)=-3 equation:

8x(2x-9)=-3

We move all terms to the left:

8x(2x-9)-(-3)=0

We add all the numbers together, and all the variables

8x(2x-9)+3=0

We multiply parentheses

16x^2-72x+3=0

a = 16; b = -72; c = +3;
Δ = b2-4ac
Δ = -722-4·16·3
Δ = 4992
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:

$\sqrt{\Delta}=\sqrt{4992}=\sqrt{64*78}=\sqrt{64}*\sqrt{78}=8\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{78}}{2*16}=\frac{72-8\sqrt{78}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{78}}{2*16}=\frac{72+8\sqrt{78}}{32}
$