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15+26x+8x^2=6
We move all terms to the left:
15+26x+8x^2-(6)=0
We add all the numbers together, and all the variables
8x^2+26x+9=0
a = 8; b = 26; c = +9;
Δ = b2-4ac
Δ = 262-4·8·9
Δ = 388
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{97}}{2*8}=\frac{-26-2\sqrt{97}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{97}}{2*8}=\frac{-26+2\sqrt{97}}{16} $
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