2x^2-9x=-6.75

Solution for 2x^2-9x=-6.75 equation:

2x^2-9x=-6.75

We move all terms to the left:

2x^2-9x-(-6.75)=0

We add all the numbers together, and all the variables

2x^2-9x+6.75=0

a = 2; b = -9; c = +6.75;
Δ = b2-4ac
Δ = -92-4·2·6.75
Δ = 27
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:

$\sqrt{\Delta}=\sqrt{27}=\sqrt{9*3}=\sqrt{9}*\sqrt{3}=3\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{3}}{2*2}=\frac{9-3\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{3}}{2*2}=\frac{9+3\sqrt{3}}{4}
$