78=3x+3x^2

Solution for 78=3x+3x^2 equation:

78=3x+3x^2

We move all terms to the left:

78-(3x+3x^2)=0

We get rid of parentheses

-3x^2-3x+78=0

a = -3; b = -3; c = +78;
Δ = b2-4ac
Δ = -32-4·(-3)·78
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{105}}{2*-3}=\frac{3-3\sqrt{105}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{105}}{2*-3}=\frac{3+3\sqrt{105}}{-6}
$