7x(x+5)=49

Solution for 7x(x+5)=49 equation:

7x(x+5)=49

We move all terms to the left:

7x(x+5)-(49)=0

We multiply parentheses

7x^2+35x-49=0

a = 7; b = 35; c = -49;
Δ = b2-4ac
Δ = 352-4·7·(-49)
Δ = 2597
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:

$\sqrt{\Delta}=\sqrt{2597}=\sqrt{49*53}=\sqrt{49}*\sqrt{53}=7\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-7\sqrt{53}}{2*7}=\frac{-35-7\sqrt{53}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+7\sqrt{53}}{2*7}=\frac{-35+7\sqrt{53}}{14}
$