(a-1)2+2a2=(2a+1)2

Solution for (a-1)2+2a2=(2a+1)2 equation:

(a-1)2+2a^2=(2a+1)2

We move all terms to the left:

(a-1)2+2a^2-((2a+1)2)=0

We multiply parentheses

2a^2+2a-((2a+1)2)-2=0


We calculate terms in parentheses: -((2a+1)2), so:

(2a+1)2

We multiply parentheses

4a+2

Back to the equation:

-(4a+2)


We get rid of parentheses

2a^2+2a-4a-2-2=0

We add all the numbers together, and all the variables

2a^2-2a-4=0

a = 2; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·2·(-4)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*2}=\frac{-4}{4}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*2}=\frac{8}{4}
=2
$