3x^2-9x+9/8=0

Solution for 3x^2-9x+9/8=0 equation:

3x^2-9x+9/8=0

We multiply all the terms by the denominator


3x^2*8-9x*8+9=0

Wy multiply elements

24x^2-72x+9=0

a = 24; b = -72; c = +9;
Δ = b2-4ac
Δ = -722-4·24·9
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{30}}{2*24}=\frac{72-12\sqrt{30}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{30}}{2*24}=\frac{72+12\sqrt{30}}{48}
$