x^2+1=4(2x-1)

Solution for x^2+1=4(2x-1) equation:

x^2+1=4(2x-1)

We move all terms to the left:

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


We calculate terms in parentheses: -(4(2x-1)), so:

4(2x-1)

We multiply parentheses

8x-4

Back to the equation:

-(8x-4)


We get rid of parentheses

x^2-8x+4+1=0

We add all the numbers together, and all the variables

x^2-8x+5=0

a = 1; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·1·5
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{11}}{2*1}=\frac{8-2\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{11}}{2*1}=\frac{8+2\sqrt{11}}{2}
$