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38x(x-1)=741
We move all terms to the left:
38x(x-1)-(741)=0
We multiply parentheses
38x^2-38x-741=0
a = 38; b = -38; c = -741;
Δ = b2-4ac
Δ = -382-4·38·(-741)
Δ = 114076
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{114076}=\sqrt{1444*79}=\sqrt{1444}*\sqrt{79}=38\sqrt{79}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38\sqrt{79}}{2*38}=\frac{38-38\sqrt{79}}{76} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38\sqrt{79}}{2*38}=\frac{38+38\sqrt{79}}{76} $
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