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2x(x+5)-7=17
We move all terms to the left:
2x(x+5)-7-(17)=0
We add all the numbers together, and all the variables
2x(x+5)-24=0
We multiply parentheses
2x^2+10x-24=0
a = 2; b = 10; c = -24;
Δ = b2-4ac
Δ = 102-4·2·(-24)
Δ = 292
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{73}}{2*2}=\frac{-10-2\sqrt{73}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{73}}{2*2}=\frac{-10+2\sqrt{73}}{4} $
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