(y^2-y+2)=(5y-2)

Solution for (y^2-y+2)=(5y-2) equation:

(y^2-y+2)=(5y-2)

We move all terms to the left:

(y^2-y+2)-((5y-2))=0

We get rid of parentheses

y^2-y-((5y-2))+2=0


We calculate terms in parentheses: -((5y-2)), so:

(5y-2)

We get rid of parentheses

5y-2

Back to the equation:

-(5y-2)


We add all the numbers together, and all the variables

y^2-1y-(5y-2)+2=0

We get rid of parentheses

y^2-1y-5y+2+2=0

We add all the numbers together, and all the variables

y^2-6y+4=0

a = 1; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·1·4
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{5}}{2*1}=\frac{6-2\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{5}}{2*1}=\frac{6+2\sqrt{5}}{2}
$