1/3x+8.1=5x+7.7

Solution for 1/3x+8.1=5x+7.7 equation:

1/3x+8.1=5x+7.7

We move all terms to the left:

1/3x+8.1-(5x+7.7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-5x-7.7+8.1=0

We multiply all the terms by the denominator


-5x*3x-(7.7)*3x+(8.1)*3x+1=0

We multiply parentheses

-5x*3x-23.1x+24.3x+1=0

Wy multiply elements

-15x^2-23.1x+24.3x+1=0

We add all the numbers together, and all the variables

-15x^2+1.2x+1=0

a = -15; b = 1.2; c = +1;
Δ = b2-4ac
Δ = 1.22-4·(-15)·1
Δ = 61.44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.2)-\sqrt{61.44}}{2*-15}=\frac{-1.2-\sqrt{61.44}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.2)+\sqrt{61.44}}{2*-15}=\frac{-1.2+\sqrt{61.44}}{-30}
$