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5(y+2)3y=8y+10
We move all terms to the left:
5(y+2)3y-(8y+10)=0
We multiply parentheses
15y^2+30y-(8y+10)=0
We get rid of parentheses
15y^2+30y-8y-10=0
We add all the numbers together, and all the variables
15y^2+22y-10=0
a = 15; b = 22; c = -10;
Δ = b2-4ac
Δ = 222-4·15·(-10)
Δ = 1084
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{271}}{2*15}=\frac{-22-2\sqrt{271}}{30} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{271}}{2*15}=\frac{-22+2\sqrt{271}}{30} $
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