3/8x-9.2=7.4+1.4x

Solution for 3/8x-9.2=7.4+1.4x equation:

3/8x-9.2=7.4+1.4x

We move all terms to the left:

3/8x-9.2-(7.4+1.4x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

3/8x-(1.4x+7.4)-9.2=0

We get rid of parentheses

3/8x-1.4x-7.4-9.2=0

We multiply all the terms by the denominator


-(1.4x)*8x-(7.4)*8x-(9.2)*8x+3=0

We add all the numbers together, and all the variables

-(+1.4x)*8x-(7.4)*8x-(9.2)*8x+3=0

We multiply parentheses

-8x^2-59.2x-73.6x+3=0

We add all the numbers together, and all the variables

-8x^2-132.8x+3=0

a = -8; b = -132.8; c = +3;
Δ = b2-4ac
Δ = -132.82-4·(-8)·3
Δ = 17731.84
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{-(-132.8)-\sqrt{17731.84}}{2*-8}=\frac{132.8-\sqrt{17731.84}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132.8)+\sqrt{17731.84}}{2*-8}=\frac{132.8+\sqrt{17731.84}}{-16}
$