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0=8x^2+24x-19
We move all terms to the left:
0-(8x^2+24x-19)=0
We add all the numbers together, and all the variables
-(8x^2+24x-19)=0
We get rid of parentheses
-8x^2-24x+19=0
a = -8; b = -24; c = +19;
Δ = b2-4ac
Δ = -242-4·(-8)·19
Δ = 1184
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{74}}{2*-8}=\frac{24-4\sqrt{74}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{74}}{2*-8}=\frac{24+4\sqrt{74}}{-16} $
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