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7x(5x-7)=1
We move all terms to the left:
7x(5x-7)-(1)=0
We multiply parentheses
35x^2-49x-1=0
a = 35; b = -49; c = -1;
Δ = b2-4ac
Δ = -492-4·35·(-1)
Δ = 2541
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2541}=\sqrt{121*21}=\sqrt{121}*\sqrt{21}=11\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-11\sqrt{21}}{2*35}=\frac{49-11\sqrt{21}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+11\sqrt{21}}{2*35}=\frac{49+11\sqrt{21}}{70} $
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