4x^2+12x+9=62

Solution for 4x^2+12x+9=62 equation:

4x^2+12x+9=62

We move all terms to the left:

4x^2+12x+9-(62)=0

We add all the numbers together, and all the variables

4x^2+12x-53=0

a = 4; b = 12; c = -53;
Δ = b2-4ac
Δ = 122-4·4·(-53)
Δ = 992
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:

$\sqrt{\Delta}=\sqrt{992}=\sqrt{16*62}=\sqrt{16}*\sqrt{62}=4\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{62}}{2*4}=\frac{-12-4\sqrt{62}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{62}}{2*4}=\frac{-12+4\sqrt{62}}{8}
$