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2x(x-3)-7=18-5(x-4)
We move all terms to the left:
2x(x-3)-7-(18-5(x-4))=0
We multiply parentheses
2x^2-6x-(18-5(x-4))-7=0
We calculate terms in parentheses: -(18-5(x-4)), so:We get rid of parentheses
18-5(x-4)
determiningTheFunctionDomain -5(x-4)+18
We multiply parentheses
-5x+20+18
We add all the numbers together, and all the variables
-5x+38
Back to the equation:
-(-5x+38)
2x^2-6x+5x-38-7=0
We add all the numbers together, and all the variables
2x^2-1x-45=0
a = 2; b = -1; c = -45;
Δ = b2-4ac
Δ = -12-4·2·(-45)
Δ = 361
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{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*2}=\frac{-18}{4} =-4+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*2}=\frac{20}{4} =5 $
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