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(x-32)(5/9)=x
We move all terms to the left:
(x-32)(5/9)-(x)=0
We add all the numbers together, and all the variables
(x-32)(+5/9)-x=0
We add all the numbers together, and all the variables
-1x+(x-32)(+5/9)=0
We multiply parentheses ..
(+5x^2-32*5/9)-1x=0
We multiply all the terms by the denominator
(+5x^2-32*5-1x*9)=0
We get rid of parentheses
5x^2-1x*9-32*5=0
We add all the numbers together, and all the variables
5x^2-1x*9-160=0
Wy multiply elements
5x^2-9x-160=0
a = 5; b = -9; c = -160;
Δ = b2-4ac
Δ = -92-4·5·(-160)
Δ = 3281
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{3281}}{2*5}=\frac{9-\sqrt{3281}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{3281}}{2*5}=\frac{9+\sqrt{3281}}{10} $
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