5.1+(7+y)y=4

Solution for 5.1+(7+y)y=4 equation:

5.1+(7+y)y=4

We move all terms to the left:

5.1+(7+y)y-(4)=0

We add all the numbers together, and all the variables

(y+7)y+5.1-4=0

We add all the numbers together, and all the variables

(y+7)y+1.1=0

We multiply parentheses

y^2+7y+1.1=0

a = 1; b = 7; c = +1.1;
Δ = b2-4ac
Δ = 72-4·1·1.1
Δ = 44.6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{44.6}}{2*1}=\frac{-7-\sqrt{44.6}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{44.6}}{2*1}=\frac{-7+\sqrt{44.6}}{2}
$