(7-3x)(x+4)=4

Solution for (7-3x)(x+4)=4 equation:

(7-3x)(x+4)=4

We move all terms to the left:

(7-3x)(x+4)-(4)=0

We add all the numbers together, and all the variables

(-3x+7)(x+4)-4=0

We multiply parentheses ..

(-3x^2-12x+7x+28)-4=0

We get rid of parentheses

-3x^2-12x+7x+28-4=0

We add all the numbers together, and all the variables

-3x^2-5x+24=0

a = -3; b = -5; c = +24;
Δ = b2-4ac
Δ = -52-4·(-3)·24
Δ = 313
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{313}}{2*-3}=\frac{5-\sqrt{313}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{313}}{2*-3}=\frac{5+\sqrt{313}}{-6}
$