25x^2=40x-16/5

Solution for 25x^2=40x-16/5 equation:

25x^2=40x-16/5

We move all terms to the left:

25x^2-(40x-16/5)=0

We add all the numbers together, and all the variables

25x^2-(+40x-16/5)=0

We get rid of parentheses

25x^2-40x+16/5=0

We multiply all the terms by the denominator


25x^2*5-40x*5+16=0

Wy multiply elements

125x^2-200x+16=0

a = 125; b = -200; c = +16;
Δ = b2-4ac
Δ = -2002-4·125·16
Δ = 32000
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:

$\sqrt{\Delta}=\sqrt{32000}=\sqrt{6400*5}=\sqrt{6400}*\sqrt{5}=80\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-80\sqrt{5}}{2*125}=\frac{200-80\sqrt{5}}{250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+80\sqrt{5}}{2*125}=\frac{200+80\sqrt{5}}{250}
$