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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2-5x^2-5x-(3x+1)+4=0

We get rid of parentheses

2x^2-5x^2-5x-3x-1+4=0

We add all the numbers together, and all the variables

-3x^2-8x+3=0

a = -3; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-3)·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10}{2*-3}=\frac{-2}{-6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*-3}=\frac{18}{-6}
=-3
$