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5(x-1)4x+3=79
We move all terms to the left:
5(x-1)4x+3-(79)=0
We add all the numbers together, and all the variables
5(x-1)4x-76=0
We multiply parentheses
20x^2-20x-76=0
a = 20; b = -20; c = -76;
Δ = b2-4ac
Δ = -202-4·20·(-76)
Δ = 6480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-36\sqrt{5}}{2*20}=\frac{20-36\sqrt{5}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+36\sqrt{5}}{2*20}=\frac{20+36\sqrt{5}}{40} $
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