4w2+12w+9=49

Solution for 4w2+12w+9=49 equation:

4w^2+12w+9=49

We move all terms to the left:

4w^2+12w+9-(49)=0

We add all the numbers together, and all the variables

4w^2+12w-40=0

a = 4; b = 12; c = -40;
Δ = b2-4ac
Δ = 122-4·4·(-40)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-28}{2*4}=\frac{-40}{8}
=-5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+28}{2*4}=\frac{16}{8}
=2
$