6x^2-43x+9=2

Solution for 6x^2-43x+9=2 equation:

6x^2-43x+9=2

We move all terms to the left:

6x^2-43x+9-(2)=0

We add all the numbers together, and all the variables

6x^2-43x+7=0

a = 6; b = -43; c = +7;
Δ = b2-4ac
Δ = -432-4·6·7
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-41}{2*6}=\frac{2}{12}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+41}{2*6}=\frac{84}{12}
=7
$