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2x^2-14x+24=09
We move all terms to the left:
2x^2-14x+24-(09)=0
We add all the numbers together, and all the variables
2x^2-14x+15=0
a = 2; b = -14; c = +15;
Δ = b2-4ac
Δ = -142-4·2·15
Δ = 76
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{19}}{2*2}=\frac{14-2\sqrt{19}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{19}}{2*2}=\frac{14+2\sqrt{19}}{4} $
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