7x(x+9)=77

Solution for 7x(x+9)=77 equation:

7x(x+9)=77

We move all terms to the left:

7x(x+9)-(77)=0

We multiply parentheses

7x^2+63x-77=0

a = 7; b = 63; c = -77;
Δ = b2-4ac
Δ = 632-4·7·(-77)
Δ = 6125
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:

$\sqrt{\Delta}=\sqrt{6125}=\sqrt{1225*5}=\sqrt{1225}*\sqrt{5}=35\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-35\sqrt{5}}{2*7}=\frac{-63-35\sqrt{5}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+35\sqrt{5}}{2*7}=\frac{-63+35\sqrt{5}}{14}
$