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((5x^2)/125)=25^x
We move all terms to the left:
((5x^2)/125)-(25^x)=0
We get rid of parentheses
5x^2/125-25^x=0
We multiply all the terms by the denominator
5x^2-25^x*125=0
Wy multiply elements
5x^2-3125x=0
a = 5; b = -3125; c = 0;
Δ = b2-4ac
Δ = -31252-4·5·0
Δ = 9765625
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{9765625}=3125$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3125)-3125}{2*5}=\frac{0}{10} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3125)+3125}{2*5}=\frac{6250}{10} =625 $
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