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(5x-1)(7x-1)=93
We move all terms to the left:
(5x-1)(7x-1)-(93)=0
We multiply parentheses ..
(+35x^2-5x-7x+1)-93=0
We get rid of parentheses
35x^2-5x-7x+1-93=0
We add all the numbers together, and all the variables
35x^2-12x-92=0
a = 35; b = -12; c = -92;
Δ = b2-4ac
Δ = -122-4·35·(-92)
Δ = 13024
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13024}=\sqrt{16*814}=\sqrt{16}*\sqrt{814}=4\sqrt{814}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{814}}{2*35}=\frac{12-4\sqrt{814}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{814}}{2*35}=\frac{12+4\sqrt{814}}{70} $
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