7x(x+4)=18

Solution for 7x(x+4)=18 equation:

7x(x+4)=18

We move all terms to the left:

7x(x+4)-(18)=0

We multiply parentheses

7x^2+28x-18=0

a = 7; b = 28; c = -18;
Δ = b2-4ac
Δ = 282-4·7·(-18)
Δ = 1288
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:

$\sqrt{\Delta}=\sqrt{1288}=\sqrt{4*322}=\sqrt{4}*\sqrt{322}=2\sqrt{322}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{322}}{2*7}=\frac{-28-2\sqrt{322}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{322}}{2*7}=\frac{-28+2\sqrt{322}}{14}
$