(5+7)5=(4+y)y

Solution for (5+7)5=(4+y)y equation:

(5+7)5=(4+y)y

We move all terms to the left:

(5+7)5-((4+y)y)=0

We add all the numbers together, and all the variables

-((y+4)y)+125=0


We calculate terms in parentheses: -((y+4)y), so:

(y+4)y

We multiply parentheses

y^2+4y

Back to the equation:

-(y^2+4y)


We get rid of parentheses

-y^2-4y+125=0

We add all the numbers together, and all the variables

-1y^2-4y+125=0

a = -1; b = -4; c = +125;
Δ = b2-4ac
Δ = -42-4·(-1)·125
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{129}}{2*-1}=\frac{4-2\sqrt{129}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{129}}{2*-1}=\frac{4+2\sqrt{129}}{-2}
$