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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

-2x^2-2x-3x-1=0

We add all the numbers together, and all the variables

-2x^2-5x-1=0

a = -2; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·(-2)·(-1)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{17}}{2*-2}=\frac{5-\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{17}}{2*-2}=\frac{5+\sqrt{17}}{-4}
$