47-3*5^2x-4*5^x=-28-4*5^x

Solution for 47-3*5^2x-4*5^x=-28-4*5^x equation:

47-3*5^2x-4*5^x=-28-4*5^x

We move all terms to the left:

47-3*5^2x-4*5^x-(-28-4*5^x)=0

Wy multiply elements

-15x^2-20x-(-28-4*5^x)+47=0

We get rid of parentheses

-15x^2-20x+4*5^x+28+47=0

We add all the numbers together, and all the variables

-15x^2-20x+4*5^x+75=0

Wy multiply elements

-15x^2-20x+20x+75=0

We add all the numbers together, and all the variables

-15x^2+75=0

a = -15; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-15)·75
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{5}}{2*-15}=\frac{0-30\sqrt{5}}{-30}
=-\frac{30\sqrt{5}}{-30}
=-\frac{\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{5}}{2*-15}=\frac{0+30\sqrt{5}}{-30}
=\frac{30\sqrt{5}}{-30}
=\frac{\sqrt{5}}{-1}
$