0.8x-8=9/25x+3,x

Solution for 0.8x-8=9/25x+3,x equation:

0.8x-8=9/25x+3.x

We move all terms to the left:

0.8x-8-(9/25x+3.x)=0


Domain of the equation: 25x+3.x)!=0

x∈R


We add all the numbers together, and all the variables

0.8x-(+3.x+9/25x)-8=0

We get rid of parentheses

0.8x-3.x-9/25x-8=0

We multiply all the terms by the denominator


(0.8x)*25x-(3.x)*25x-8*25x-9=0

We add all the numbers together, and all the variables

(+0.8x)*25x-(+3.x)*25x-8*25x-9=0

We multiply parentheses

0x^2-75x^2-8*25x-9=0

Wy multiply elements

0x^2-75x^2-200x-9=0

We add all the numbers together, and all the variables

-74x^2-200x-9=0

a = -74; b = -200; c = -9;
Δ = b2-4ac
Δ = -2002-4·(-74)·(-9)
Δ = 37336
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:

$\sqrt{\Delta}=\sqrt{37336}=\sqrt{4*9334}=\sqrt{4}*\sqrt{9334}=2\sqrt{9334}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-2\sqrt{9334}}{2*-74}=\frac{200-2\sqrt{9334}}{-148}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+2\sqrt{9334}}{2*-74}=\frac{200+2\sqrt{9334}}{-148}
$