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-2x(-x+11)=-13+2x=-9
We move all terms to the left:
-2x(-x+11)-(-13+2x)=0
We add all the numbers together, and all the variables
-2x(-1x+11)-(2x-13)=0
We multiply parentheses
2x^2-22x-(2x-13)=0
We get rid of parentheses
2x^2-22x-2x+13=0
We add all the numbers together, and all the variables
2x^2-24x+13=0
a = 2; b = -24; c = +13;
Δ = b2-4ac
Δ = -242-4·2·13
Δ = 472
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{118}}{2*2}=\frac{24-2\sqrt{118}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{118}}{2*2}=\frac{24+2\sqrt{118}}{4} $
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