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5x^2+51x=-14
We move all terms to the left:
5x^2+51x-(-14)=0
We add all the numbers together, and all the variables
5x^2+51x+14=0
a = 5; b = 51; c = +14;
Δ = b2-4ac
Δ = 512-4·5·14
Δ = 2321
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{-(51)-\sqrt{2321}}{2*5}=\frac{-51-\sqrt{2321}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{2321}}{2*5}=\frac{-51+\sqrt{2321}}{10} $
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