4w+9=4w^2+14w+12

Solution for 4w+9=4w^2+14w+12 equation:

4w+9=4w^2+14w+12

We move all terms to the left:

4w+9-(4w^2+14w+12)=0

We get rid of parentheses

-4w^2+4w-14w-12+9=0

We add all the numbers together, and all the variables

-4w^2-10w-3=0

a = -4; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·(-4)·(-3)
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{13}}{2*-4}=\frac{10-2\sqrt{13}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{13}}{2*-4}=\frac{10+2\sqrt{13}}{-8}
$