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12x^2+5x+4=46
We move all terms to the left:
12x^2+5x+4-(46)=0
We add all the numbers together, and all the variables
12x^2+5x-42=0
a = 12; b = 5; c = -42;
Δ = b2-4ac
Δ = 52-4·12·(-42)
Δ = 2041
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{2041}}{2*12}=\frac{-5-\sqrt{2041}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{2041}}{2*12}=\frac{-5+\sqrt{2041}}{24} $
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