3x2+9x-4=5

Solution for 3x2+9x-4=5 equation:

3x^2+9x-4=5

We move all terms to the left:

3x^2+9x-4-(5)=0

We add all the numbers together, and all the variables

3x^2+9x-9=0

a = 3; b = 9; c = -9;
Δ = b2-4ac
Δ = 92-4·3·(-9)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{21}}{2*3}=\frac{-9-3\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{21}}{2*3}=\frac{-9+3\sqrt{21}}{6}
$