0=-14x^2+74x-12

Solution for 0=-14x^2+74x-12 equation:

0=-14x^2+74x-12

We move all terms to the left:

0-(-14x^2+74x-12)=0

We add all the numbers together, and all the variables

-(-14x^2+74x-12)=0

We get rid of parentheses

14x^2-74x+12=0

a = 14; b = -74; c = +12;
Δ = b2-4ac
Δ = -742-4·14·12
Δ = 4804
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:

$\sqrt{\Delta}=\sqrt{4804}=\sqrt{4*1201}=\sqrt{4}*\sqrt{1201}=2\sqrt{1201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{1201}}{2*14}=\frac{74-2\sqrt{1201}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{1201}}{2*14}=\frac{74+2\sqrt{1201}}{28}
$