x^2-x-3+x^2+2x+2=2(2x^2-46)

Solution for x^2-x-3+x^2+2x+2=2(2x^2-46) equation:

x^2-x-3+x^2+2x+2=2(2x^2-46)

We move all terms to the left:

x^2-x-3+x^2+2x+2-(2(2x^2-46))=0

We add all the numbers together, and all the variables

2x^2+x-(2(2x^2-46))-1=0


We calculate terms in parentheses: -(2(2x^2-46)), so:

2(2x^2-46)

We multiply parentheses

4x^2-92

Back to the equation:

-(4x^2-92)


We get rid of parentheses

2x^2-4x^2+x+92-1=0

We add all the numbers together, and all the variables

-2x^2+x+91=0

a = -2; b = 1; c = +91;
Δ = b2-4ac
Δ = 12-4·(-2)·91
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-27}{2*-2}=\frac{-28}{-4}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+27}{2*-2}=\frac{26}{-4}
=-6+1/2
$