2x^2-9x+12=22

Solution for 2x^2-9x+12=22 equation:

2x^2-9x+12=22

We move all terms to the left:

2x^2-9x+12-(22)=0

We add all the numbers together, and all the variables

2x^2-9x-10=0

a = 2; b = -9; c = -10;
Δ = b2-4ac
Δ = -92-4·2·(-10)
Δ = 161
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{161}}{2*2}=\frac{9-\sqrt{161}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{161}}{2*2}=\frac{9+\sqrt{161}}{4}
$