3x^2-6x-3=75

Solution for 3x^2-6x-3=75 equation:

3x^2-6x-3=75

We move all terms to the left:

3x^2-6x-3-(75)=0

We add all the numbers together, and all the variables

3x^2-6x-78=0

a = 3; b = -6; c = -78;
Δ = b2-4ac
Δ = -62-4·3·(-78)
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18\sqrt{3}}{2*3}=\frac{6-18\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18\sqrt{3}}{2*3}=\frac{6+18\sqrt{3}}{6}
$