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3x-7=-12x^2
We move all terms to the left:
3x-7-(-12x^2)=0
We get rid of parentheses
12x^2+3x-7=0
a = 12; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·12·(-7)
Δ = 345
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{-(3)-\sqrt{345}}{2*12}=\frac{-3-\sqrt{345}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{345}}{2*12}=\frac{-3+\sqrt{345}}{24} $
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