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(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} $
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