2x(x-7)+2(x-3)=0

Solution for 2x(x-7)+2(x-3)=0 equation:

2x(x-7)+2(x-3)=0

We multiply parentheses

2x^2-14x+2x-6=0

We add all the numbers together, and all the variables

2x^2-12x-6=0

a = 2; b = -12; c = -6;
Δ = b2-4ac
Δ = -122-4·2·(-6)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*2}=\frac{12-8\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*2}=\frac{12+8\sqrt{3}}{4}
$