2x(x-3)=45

Solution for 2x(x-3)=45 equation:

2x(x-3)=45

We move all terms to the left:

2x(x-3)-(45)=0

We multiply parentheses

2x^2-6x-45=0

a = 2; b = -6; c = -45;
Δ = b2-4ac
Δ = -62-4·2·(-45)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{11}}{2*2}=\frac{6-6\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{11}}{2*2}=\frac{6+6\sqrt{11}}{4}
$