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10y-6y(2)=2
We move all terms to the left:
10y-6y(2)-(2)=0
We add all the numbers together, and all the variables
-6y^2+10y-2=0
a = -6; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·(-6)·(-2)
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*-6}=\frac{-10-2\sqrt{13}}{-12} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*-6}=\frac{-10+2\sqrt{13}}{-12} $
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