7=3x^2-32x+76

Solution for 7=3x^2-32x+76 equation:

7=3x^2-32x+76

We move all terms to the left:

7-(3x^2-32x+76)=0

We get rid of parentheses

-3x^2+32x-76+7=0

We add all the numbers together, and all the variables

-3x^2+32x-69=0

a = -3; b = 32; c = -69;
Δ = b2-4ac
Δ = 322-4·(-3)·(-69)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-14}{2*-3}=\frac{-46}{-6}
=7+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+14}{2*-3}=\frac{-18}{-6}
=+3
$