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-17x=5-12x^2
We move all terms to the left:
-17x-(5-12x^2)=0
We get rid of parentheses
12x^2-17x-5=0
a = 12; b = -17; c = -5;
Δ = b2-4ac
Δ = -172-4·12·(-5)
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-23}{2*12}=\frac{-6}{24} =-1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+23}{2*12}=\frac{40}{24} =1+2/3 $
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