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5^2x/5^x+5=25/625
We move all terms to the left:
5^2x/5^x+5-(25/625)=0
Domain of the equation: 5^x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5^2x/5^x+5-(+25/625)=0
We get rid of parentheses
5^2x/5^x+5-25/625=0
We calculate fractions
3125x^2/3125x+(-125x)/3125x+5=0
We multiply all the terms by the denominator
3125x^2+(-125x)+5*3125x=0
Wy multiply elements
3125x^2+(-125x)+15625x=0
We get rid of parentheses
3125x^2-125x+15625x=0
We add all the numbers together, and all the variables
3125x^2+15500x=0
a = 3125; b = 15500; c = 0;
Δ = b2-4ac
Δ = 155002-4·3125·0
Δ = 240250000
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{240250000}=15500$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15500)-15500}{2*3125}=\frac{-31000}{6250} =-4+24/25 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15500)+15500}{2*3125}=\frac{0}{6250} =0 $
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