4c^2+12c+9=7

Solution for 4c^2+12c+9=7 equation:

4c^2+12c+9=7

We move all terms to the left:

4c^2+12c+9-(7)=0

We add all the numbers together, and all the variables

4c^2+12c+2=0

a = 4; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·4·2
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{7}}{2*4}=\frac{-12-4\sqrt{7}}{8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{7}}{2*4}=\frac{-12+4\sqrt{7}}{8}
$