78=30x-2x^2

Solution for 78=30x-2x^2 equation:

78=30x-2x^2

We move all terms to the left:

78-(30x-2x^2)=0

We get rid of parentheses

2x^2-30x+78=0

a = 2; b = -30; c = +78;
Δ = b2-4ac
Δ = -302-4·2·78
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{69}}{2*2}=\frac{30-2\sqrt{69}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{69}}{2*2}=\frac{30+2\sqrt{69}}{4}
$