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2x(x-5)=2-(7-x)
We move all terms to the left:
2x(x-5)-(2-(7-x))=0
We add all the numbers together, and all the variables
2x(x-5)-(2-(-1x+7))=0
We multiply parentheses
2x^2-10x-(2-(-1x+7))=0
We calculate terms in parentheses: -(2-(-1x+7)), so:We get rid of parentheses
2-(-1x+7)
determiningTheFunctionDomain -(-1x+7)+2
We get rid of parentheses
1x-7+2
We add all the numbers together, and all the variables
x-5
Back to the equation:
-(x-5)
2x^2-10x-x+5=0
We add all the numbers together, and all the variables
2x^2-11x+5=0
a = 2; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·2·5
Δ = 81
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-9}{2*2}=\frac{2}{4} =1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*2}=\frac{20}{4} =5 $
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