7x(x+5)+1=15

Solution for 7x(x+5)+1=15 equation:

7x(x+5)+1=15

We move all terms to the left:

7x(x+5)+1-(15)=0

We add all the numbers together, and all the variables

7x(x+5)-14=0

We multiply parentheses

7x^2+35x-14=0

a = 7; b = 35; c = -14;
Δ = b2-4ac
Δ = 352-4·7·(-14)
Δ = 1617
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:

$\sqrt{\Delta}=\sqrt{1617}=\sqrt{49*33}=\sqrt{49}*\sqrt{33}=7\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-7\sqrt{33}}{2*7}=\frac{-35-7\sqrt{33}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+7\sqrt{33}}{2*7}=\frac{-35+7\sqrt{33}}{14}
$