5x-3(2x+7)x=-2

Solution for 5x-3(2x+7)x=-2 equation:

5x-3(2x+7)x=-2

We move all terms to the left:

5x-3(2x+7)x-(-2)=0

We add all the numbers together, and all the variables

5x-3(2x+7)x+2=0

We multiply parentheses

-6x^2+5x-21x+2=0

We add all the numbers together, and all the variables

-6x^2-16x+2=0

a = -6; b = -16; c = +2;
Δ = b2-4ac
Δ = -162-4·(-6)·2
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{19}}{2*-6}=\frac{16-4\sqrt{19}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*-6}=\frac{16+4\sqrt{19}}{-12}
$