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12x^2+51x+45=0
a = 12; b = 51; c = +45;
Δ = b2-4ac
Δ = 512-4·12·45
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{441}=21$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-21}{2*12}=\frac{-72}{24} =-3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+21}{2*12}=\frac{-30}{24} =-1+1/4 $
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