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2y^2+11y=y^2-3y-28
We move all terms to the left:
2y^2+11y-(y^2-3y-28)=0
We get rid of parentheses
2y^2-y^2+11y+3y+28=0
We add all the numbers together, and all the variables
y^2+14y+28=0
a = 1; b = 14; c = +28;
Δ = b2-4ac
Δ = 142-4·1·28
Δ = 84
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{21}}{2*1}=\frac{-14-2\sqrt{21}}{2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{21}}{2*1}=\frac{-14+2\sqrt{21}}{2} $
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