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2+2X-1=2X(X+5)=-9
We move all terms to the left:
2+2X-1-(2X(X+5))=0
We add all the numbers together, and all the variables
2X-(2X(X+5))+1=0
We calculate terms in parentheses: -(2X(X+5)), so:We get rid of parentheses
2X(X+5)
We multiply parentheses
2X^2+10X
Back to the equation:
-(2X^2+10X)
-2X^2+2X-10X+1=0
We add all the numbers together, and all the variables
-2X^2-8X+1=0
a = -2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-2)·1
Δ = 72
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{2}}{2*-2}=\frac{8-6\sqrt{2}}{-4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*-2}=\frac{8+6\sqrt{2}}{-4} $
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