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X+(X+7)2X=34
We move all terms to the left:
X+(X+7)2X-(34)=0
We multiply parentheses
2X^2+X+14X-34=0
We add all the numbers together, and all the variables
2X^2+15X-34=0
a = 2; b = 15; c = -34;
Δ = b2-4ac
Δ = 152-4·2·(-34)
Δ = 497
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{497}}{2*2}=\frac{-15-\sqrt{497}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{497}}{2*2}=\frac{-15+\sqrt{497}}{4} $
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