5(x+1)(x+1)=625

Solution for 5(x+1)(x+1)=625 equation:

5(x+1)(x+1)=625

We move all terms to the left:

5(x+1)(x+1)-(625)=0

We multiply parentheses ..

5(+x^2+x+x+1)-625=0

We multiply parentheses

5x^2+5x+5x+5-625=0

We add all the numbers together, and all the variables

5x^2+10x-620=0

a = 5; b = 10; c = -620;
Δ = b2-4ac
Δ = 102-4·5·(-620)
Δ = 12500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12500}=\sqrt{2500*5}=\sqrt{2500}*\sqrt{5}=50\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-50\sqrt{5}}{2*5}=\frac{-10-50\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+50\sqrt{5}}{2*5}=\frac{-10+50\sqrt{5}}{10}
$