3x^2-3x-7x=-2

Solution for 3x^2-3x-7x=-2 equation:

3x^2-3x-7x=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-10x+2=0

a = 3; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·3·2
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{19}}{2*3}=\frac{10-2\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{19}}{2*3}=\frac{10+2\sqrt{19}}{6}
$