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12x+5x^2=252
We move all terms to the left:
12x+5x^2-(252)=0
a = 5; b = 12; c = -252;
Δ = b2-4ac
Δ = 122-4·5·(-252)
Δ = 5184
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{5184}=72$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-72}{2*5}=\frac{-84}{10} =-8+2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+72}{2*5}=\frac{60}{10} =6 $
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