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125^2x=5^x-3/625
We move all terms to the left:
125^2x-(5^x-3/625)=0
We get rid of parentheses
125^2x-5^x+3/625=0
We multiply all the terms by the denominator
125^2x*625-5^x*625+3=0
Wy multiply elements
78125x^2-3125x+3=0
a = 78125; b = -3125; c = +3;
Δ = b2-4ac
Δ = -31252-4·78125·3
Δ = 8828125
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8828125}=\sqrt{15625*565}=\sqrt{15625}*\sqrt{565}=125\sqrt{565}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3125)-125\sqrt{565}}{2*78125}=\frac{3125-125\sqrt{565}}{156250} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3125)+125\sqrt{565}}{2*78125}=\frac{3125+125\sqrt{565}}{156250} $
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