9x^2+12x-13=3

Solution for 9x^2+12x-13=3 equation:

9x^2+12x-13=3

We move all terms to the left:

9x^2+12x-13-(3)=0

We add all the numbers together, and all the variables

9x^2+12x-16=0

a = 9; b = 12; c = -16;
Δ = b2-4ac
Δ = 122-4·9·(-16)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{5}}{2*9}=\frac{-12-12\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{5}}{2*9}=\frac{-12+12\sqrt{5}}{18}
$