12.25+144=(y+3.5)(y+3.5)

Solution for 12.25+144=(y+3.5)(y+3.5) equation:

12.25+144=(y+3.5)(y+3.5)

We move all terms to the left:

12.25+144-((y+3.5)(y+3.5))=0

We add all the numbers together, and all the variables

-((y+3.5)(y+3.5))+156.25=0

We multiply parentheses ..

-((+y^2+3.5y+3.5y+12.25))+156.25=0


We calculate terms in parentheses: -((+y^2+3.5y+3.5y+12.25)), so:

(+y^2+3.5y+3.5y+12.25)

We get rid of parentheses

y^2+3.5y+3.5y+12.25

We add all the numbers together, and all the variables

y^2+7y+12.25

Back to the equation:

-(y^2+7y+12.25)


We get rid of parentheses

-y^2-7y-12.25+156.25=0

We add all the numbers together, and all the variables

-1y^2-7y+144=0

a = -1; b = -7; c = +144;
Δ = b2-4ac
Δ = -72-4·(-1)·144
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-25}{2*-1}=\frac{-18}{-2}
=+9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+25}{2*-1}=\frac{32}{-2}
=-16
$