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5y(7+y)-3y-5=0
We add all the numbers together, and all the variables
5y(y+7)-3y-5=0
We add all the numbers together, and all the variables
-3y+5y(y+7)-5=0
We multiply parentheses
5y^2-3y+35y-5=0
We add all the numbers together, and all the variables
5y^2+32y-5=0
a = 5; b = 32; c = -5;
Δ = b2-4ac
Δ = 322-4·5·(-5)
Δ = 1124
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{281}}{2*5}=\frac{-32-2\sqrt{281}}{10} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{281}}{2*5}=\frac{-32+2\sqrt{281}}{10} $
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