8.1(1/3x)=1/2x+7.7

Solution for 8.1(1/3x)=1/2x+7.7 equation:

8.1(1/3x)=1/2x+7.7

We move all terms to the left:

8.1(1/3x)-(1/2x+7.7)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2x+7.7)!=0

x∈R


We add all the numbers together, and all the variables

8.1(+1/3x)-(1/2x+7.7)=0

We multiply parentheses

8.1x-(1/2x+7.7)=0

We get rid of parentheses

8.1x-1/2x-7.7=0

We multiply all the terms by the denominator


(8.1x)*2x-(7.7)*2x-1=0

We add all the numbers together, and all the variables

(+8.1x)*2x-(7.7)*2x-1=0

We multiply parentheses

16x^2-15.4x-1=0

a = 16; b = -15.4; c = -1;
Δ = b2-4ac
Δ = -15.42-4·16·(-1)
Δ = 301.16
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{-(-15.4)-\sqrt{301.16}}{2*16}=\frac{15.4-\sqrt{301.16}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15.4)+\sqrt{301.16}}{2*16}=\frac{15.4+\sqrt{301.16}}{32}
$