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5x^2+14x-24=04
We move all terms to the left:
5x^2+14x-24-(04)=0
We add all the numbers together, and all the variables
5x^2+14x-28=0
a = 5; b = 14; c = -28;
Δ = b2-4ac
Δ = 142-4·5·(-28)
Δ = 756
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{21}}{2*5}=\frac{-14-6\sqrt{21}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{21}}{2*5}=\frac{-14+6\sqrt{21}}{10} $
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