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35x^2-10x=5
We move all terms to the left:
35x^2-10x-(5)=0
a = 35; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·35·(-5)
Δ = 800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20\sqrt{2}}{2*35}=\frac{10-20\sqrt{2}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20\sqrt{2}}{2*35}=\frac{10+20\sqrt{2}}{70} $
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