3/10x+9=3-0.1x

Solution for 3/10x+9=3-0.1x equation:

3/10x+9=3-0.1x

We move all terms to the left:

3/10x+9-(3-0.1x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

3/10x-(-0.1x+3)+9=0

We get rid of parentheses

3/10x+0.1x-3+9=0

We multiply all the terms by the denominator


(0.1x)*10x-3*10x+9*10x+3=0

We add all the numbers together, and all the variables

(+0.1x)*10x-3*10x+9*10x+3=0

We multiply parentheses

0x^2-3*10x+9*10x+3=0

Wy multiply elements

0x^2-30x+90x+3=0

We add all the numbers together, and all the variables

x^2+60x+3=0

a = 1; b = 60; c = +3;
Δ = b2-4ac
Δ = 602-4·1·3
Δ = 3588
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:

$\sqrt{\Delta}=\sqrt{3588}=\sqrt{4*897}=\sqrt{4}*\sqrt{897}=2\sqrt{897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{897}}{2*1}=\frac{-60-2\sqrt{897}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{897}}{2*1}=\frac{-60+2\sqrt{897}}{2}
$