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5-1*5x=6x-x2
We move all terms to the left:
5-1*5x-(6x-x2)=0
We add all the numbers together, and all the variables
-(+6x-1x^2)-1*5x+5=0
Wy multiply elements
-(+6x-1x^2)-5x+5=0
We get rid of parentheses
1x^2-6x-5x+5=0
We add all the numbers together, and all the variables
x^2-11x+5=0
a = 1; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·1·5
Δ = 101
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{-(-11)-\sqrt{101}}{2*1}=\frac{11-\sqrt{101}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{101}}{2*1}=\frac{11+\sqrt{101}}{2} $
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