9x^2+12x+4=17

Solution for 9x^2+12x+4=17 equation:

9x^2+12x+4=17

We move all terms to the left:

9x^2+12x+4-(17)=0

We add all the numbers together, and all the variables

9x^2+12x-13=0

a = 9; b = 12; c = -13;
Δ = b2-4ac
Δ = 122-4·9·(-13)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{17}}{2*9}=\frac{-12-6\sqrt{17}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{17}}{2*9}=\frac{-12+6\sqrt{17}}{18}
$