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5x(x-4)-7x=-12
We move all terms to the left:
5x(x-4)-7x-(-12)=0
We add all the numbers together, and all the variables
-7x+5x(x-4)+12=0
We multiply parentheses
5x^2-7x-20x+12=0
We add all the numbers together, and all the variables
5x^2-27x+12=0
a = 5; b = -27; c = +12;
Δ = b2-4ac
Δ = -272-4·5·12
Δ = 489
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{-(-27)-\sqrt{489}}{2*5}=\frac{27-\sqrt{489}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{489}}{2*5}=\frac{27+\sqrt{489}}{10} $
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