4(900y-5)+y2=10

Solution for 4(900y-5)+y2=10 equation:

4(900y-5)+y2=10

We move all terms to the left:

4(900y-5)+y2-(10)=0

We add all the numbers together, and all the variables

y^2+4(900y-5)-10=0

We multiply parentheses

y^2+3600y-20-10=0

We add all the numbers together, and all the variables

y^2+3600y-30=0

a = 1; b = 3600; c = -30;
Δ = b2-4ac
Δ = 36002-4·1·(-30)
Δ = 12960120
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:

$\sqrt{\Delta}=\sqrt{12960120}=\sqrt{4*3240030}=\sqrt{4}*\sqrt{3240030}=2\sqrt{3240030}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3600)-2\sqrt{3240030}}{2*1}=\frac{-3600-2\sqrt{3240030}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3600)+2\sqrt{3240030}}{2*1}=\frac{-3600+2\sqrt{3240030}}{2}
$