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5x=x2+4
We move all terms to the left:
5x-(x2+4)=0
We add all the numbers together, and all the variables
-(+x^2+4)+5x=0
We get rid of parentheses
-x^2+5x-4=0
We add all the numbers together, and all the variables
-1x^2+5x-4=0
a = -1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·(-1)·(-4)
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*-1}=\frac{-8}{-2} =+4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-1}=\frac{-2}{-2} =1 $
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