3x2-2x-5=4

Solution for 3x2-2x-5=4 equation:

3x^2-2x-5=4

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-2x-9=0

a = 3; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·3·(-9)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{7}}{2*3}=\frac{2-4\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{7}}{2*3}=\frac{2+4\sqrt{7}}{6}
$