2x*x-9x+6=0

Solution for 2x*x-9x+6=0 equation:

2x*x-9x+6=0

We add all the numbers together, and all the variables

-9x+2x*x+6=0

Wy multiply elements

2x^2-9x+6=0

a = 2; b = -9; c = +6;
Δ = b2-4ac
Δ = -92-4·2·6
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{33}}{2*2}=\frac{9-\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*2}=\frac{9+\sqrt{33}}{4}
$