6x+2x(x+2)=45

Solution for 6x+2x(x+2)=45 equation:

6x+2x(x+2)=45

We move all terms to the left:

6x+2x(x+2)-(45)=0

We multiply parentheses

2x^2+6x+4x-45=0

We add all the numbers together, and all the variables

2x^2+10x-45=0

a = 2; b = 10; c = -45;
Δ = b2-4ac
Δ = 102-4·2·(-45)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{115}}{2*2}=\frac{-10-2\sqrt{115}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{115}}{2*2}=\frac{-10+2\sqrt{115}}{4}
$