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12y^2+15y+3=176
We move all terms to the left:
12y^2+15y+3-(176)=0
We add all the numbers together, and all the variables
12y^2+15y-173=0
a = 12; b = 15; c = -173;
Δ = b2-4ac
Δ = 152-4·12·(-173)
Δ = 8529
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{-(15)-\sqrt{8529}}{2*12}=\frac{-15-\sqrt{8529}}{24} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{8529}}{2*12}=\frac{-15+\sqrt{8529}}{24} $
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