7x^2+28x=-18

Solution for 7x^2+28x=-18 equation:

7x^2+28x=-18

We move all terms to the left:

7x^2+28x-(-18)=0

We add all the numbers together, and all the variables

7x^2+28x+18=0

a = 7; b = 28; c = +18;
Δ = b2-4ac
Δ = 282-4·7·18
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{70}}{2*7}=\frac{-28-2\sqrt{70}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{70}}{2*7}=\frac{-28+2\sqrt{70}}{14}
$