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5(x-4)4x=7
We move all terms to the left:
5(x-4)4x-(7)=0
We multiply parentheses
20x^2-80x-7=0
a = 20; b = -80; c = -7;
Δ = b2-4ac
Δ = -802-4·20·(-7)
Δ = 6960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6960}=\sqrt{16*435}=\sqrt{16}*\sqrt{435}=4\sqrt{435}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{435}}{2*20}=\frac{80-4\sqrt{435}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{435}}{2*20}=\frac{80+4\sqrt{435}}{40} $
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