x/0.04x+0.07(900-x)=51

Solution for x/0.04x+0.07(900-x)=51 equation:

x/0.04x+0.07(900-x)=51

We move all terms to the left:

x/0.04x+0.07(900-x)-(51)=0


Domain of the equation: 0.04x!=0

x!=0/0.04

x!=0

x∈R


We add all the numbers together, and all the variables

x/0.04x+0.07(-1x+900)-51=0

We multiply parentheses

x/0.04x-0.07x+63-51=0

We multiply all the terms by the denominator


x-(0.07x)*0.04x+63*0.04x-51*0.04x=0

We add all the numbers together, and all the variables

x-(+0.07x)*0.04x+63*0.04x-51*0.04x=0

We multiply parentheses

-0x^2+x+63*0.04x-51*0.04x=0

Wy multiply elements

-0x^2+x+0x+0x=0

We add all the numbers together, and all the variables

-1x^2+3x=0

a = -1; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-1}=\frac{0}{-2}
=0
$