9x^2+4x-4=67

Solution for 9x^2+4x-4=67 equation:

9x^2+4x-4=67

We move all terms to the left:

9x^2+4x-4-(67)=0

We add all the numbers together, and all the variables

9x^2+4x-71=0

a = 9; b = 4; c = -71;
Δ = b2-4ac
Δ = 42-4·9·(-71)
Δ = 2572
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:

$\sqrt{\Delta}=\sqrt{2572}=\sqrt{4*643}=\sqrt{4}*\sqrt{643}=2\sqrt{643}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{643}}{2*9}=\frac{-4-2\sqrt{643}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{643}}{2*9}=\frac{-4+2\sqrt{643}}{18}
$