-x2+3=(2x-1)2

Solution for -x2+3=(2x-1)2 equation:

-x2+3=(2x-1)2

We move all terms to the left:

-x2+3-((2x-1)2)=0

We add all the numbers together, and all the variables

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


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

(2x-1)2

We multiply parentheses

4x-2

Back to the equation:

-(4x-2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-1)·5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*-1}=\frac{10}{-2}
=-5
$