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5(7y^2+1)+11y=11
We move all terms to the left:
5(7y^2+1)+11y-(11)=0
We add all the numbers together, and all the variables
11y+5(7y^2+1)-11=0
We multiply parentheses
35y^2+11y+5-11=0
We add all the numbers together, and all the variables
35y^2+11y-6=0
a = 35; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·35·(-6)
Δ = 961
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{961}=31$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-31}{2*35}=\frac{-42}{70} =-3/5 $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+31}{2*35}=\frac{20}{70} =2/7 $
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