7x(x+9)=14

Solution for 7x(x+9)=14 equation:

7x(x+9)=14

We move all terms to the left:

7x(x+9)-(14)=0

We multiply parentheses

7x^2+63x-14=0

a = 7; b = 63; c = -14;
Δ = b2-4ac
Δ = 632-4·7·(-14)
Δ = 4361
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:

$\sqrt{\Delta}=\sqrt{4361}=\sqrt{49*89}=\sqrt{49}*\sqrt{89}=7\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-7\sqrt{89}}{2*7}=\frac{-63-7\sqrt{89}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+7\sqrt{89}}{2*7}=\frac{-63+7\sqrt{89}}{14}
$