3x^2-2x-3=89

Solution for 3x^2-2x-3=89 equation:

3x^2-2x-3=89

We move all terms to the left:

3x^2-2x-3-(89)=0

We add all the numbers together, and all the variables

3x^2-2x-92=0

a = 3; b = -2; c = -92;
Δ = b2-4ac
Δ = -22-4·3·(-92)
Δ = 1108
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:

$\sqrt{\Delta}=\sqrt{1108}=\sqrt{4*277}=\sqrt{4}*\sqrt{277}=2\sqrt{277}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{277}}{2*3}=\frac{2-2\sqrt{277}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{277}}{2*3}=\frac{2+2\sqrt{277}}{6}
$