6-2x(5x+1)=3

Solution for 6-2x(5x+1)=3 equation:

6-2x(5x+1)=3

We move all terms to the left:

6-2x(5x+1)-(3)=0

We add all the numbers together, and all the variables

-2x(5x+1)+3=0

We multiply parentheses

-10x^2-2x+3=0

a = -10; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-10)·3
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*-10}=\frac{2-2\sqrt{31}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*-10}=\frac{2+2\sqrt{31}}{-20}
$