2(x-6)X=9=

Solution for 2(x-6)X=9= equation:

2(x-6)x=9=

We move all terms to the left:

2(x-6)x-(9)=0

We multiply parentheses

2x^2-12x-9=0

a = 2; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·2·(-9)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{6}}{2*2}=\frac{12-6\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{6}}{2*2}=\frac{12+6\sqrt{6}}{4}
$