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(22x-11)=(12x-8x^2)
We move all terms to the left:
(22x-11)-((12x-8x^2))=0
We get rid of parentheses
-((12x-8x^2))+22x-11=0
We calculate terms in parentheses: -((12x-8x^2)), so:We get rid of parentheses
(12x-8x^2)
We get rid of parentheses
-8x^2+12x
Back to the equation:
-(-8x^2+12x)
8x^2-12x+22x-11=0
We add all the numbers together, and all the variables
8x^2+10x-11=0
a = 8; b = 10; c = -11;
Δ = b2-4ac
Δ = 102-4·8·(-11)
Δ = 452
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{113}}{2*8}=\frac{-10-2\sqrt{113}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{113}}{2*8}=\frac{-10+2\sqrt{113}}{16} $
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