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7x(5x-2)-2=x
We move all terms to the left:
7x(5x-2)-2-(x)=0
We add all the numbers together, and all the variables
-1x+7x(5x-2)-2=0
We multiply parentheses
35x^2-1x-14x-2=0
We add all the numbers together, and all the variables
35x^2-15x-2=0
a = 35; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·35·(-2)
Δ = 505
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{505}}{2*35}=\frac{15-\sqrt{505}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{505}}{2*35}=\frac{15+\sqrt{505}}{70} $
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