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10(y+5)y=-7
We move all terms to the left:
10(y+5)y-(-7)=0
We add all the numbers together, and all the variables
10(y+5)y+7=0
We multiply parentheses
10y^2+50y+7=0
a = 10; b = 50; c = +7;
Δ = b2-4ac
Δ = 502-4·10·7
Δ = 2220
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2220}=\sqrt{4*555}=\sqrt{4}*\sqrt{555}=2\sqrt{555}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{555}}{2*10}=\frac{-50-2\sqrt{555}}{20} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{555}}{2*10}=\frac{-50+2\sqrt{555}}{20} $
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