7x^2+12x=-3

Solution for 7x^2+12x=-3 equation:

7x^2+12x=-3

We move all terms to the left:

7x^2+12x-(-3)=0

We add all the numbers together, and all the variables

7x^2+12x+3=0

a = 7; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·7·3
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{15}}{2*7}=\frac{-12-2\sqrt{15}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{15}}{2*7}=\frac{-12+2\sqrt{15}}{14}
$