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(0.5y+4)(2y-6)=0
We multiply parentheses ..
(+0y^2+0y+8y-24)=0
We get rid of parentheses
0y^2+0y+8y-24=0
We add all the numbers together, and all the variables
y^2+9y-24=0
a = 1; b = 9; c = -24;
Δ = b2-4ac
Δ = 92-4·1·(-24)
Δ = 177
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{177}}{2*1}=\frac{-9-\sqrt{177}}{2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{177}}{2*1}=\frac{-9+\sqrt{177}}{2} $
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