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-x+5=5(x-5)x=
We move all terms to the left:
-x+5-(5(x-5)x)=0
We add all the numbers together, and all the variables
-1x-(5(x-5)x)+5=0
We calculate terms in parentheses: -(5(x-5)x), so:We get rid of parentheses
5(x-5)x
We multiply parentheses
5x^2-25x
Back to the equation:
-(5x^2-25x)
-5x^2-1x+25x+5=0
We add all the numbers together, and all the variables
-5x^2+24x+5=0
a = -5; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·(-5)·5
Δ = 676
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{676}=26$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-26}{2*-5}=\frac{-50}{-10} =+5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+26}{2*-5}=\frac{2}{-10} =-1/5 $
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