(3x+1)(x-4)=66

Solution for (3x+1)(x-4)=66 equation:

(3x+1)(x-4)=66

We move all terms to the left:

(3x+1)(x-4)-(66)=0

We multiply parentheses ..

(+3x^2-12x+x-4)-66=0

We get rid of parentheses

3x^2-12x+x-4-66=0

We add all the numbers together, and all the variables

3x^2-11x-70=0

a = 3; b = -11; c = -70;
Δ = b2-4ac
Δ = -112-4·3·(-70)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-31}{2*3}=\frac{-20}{6}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*3}=\frac{42}{6}
=7
$