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20=7x^2+9x+6
We move all terms to the left:
20-(7x^2+9x+6)=0
We get rid of parentheses
-7x^2-9x-6+20=0
We add all the numbers together, and all the variables
-7x^2-9x+14=0
a = -7; b = -9; c = +14;
Δ = b2-4ac
Δ = -92-4·(-7)·14
Δ = 473
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{-(-9)-\sqrt{473}}{2*-7}=\frac{9-\sqrt{473}}{-14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{473}}{2*-7}=\frac{9+\sqrt{473}}{-14} $
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