3/8x-(-1-9.7x)=2.6+13.3x

Solution for 3/8x-(-1-9.7x)=2.6+13.3x equation:

3/8x-(-1-9.7x)=2.6+13.3x

We move all terms to the left:

3/8x-(-1-9.7x)-(2.6+13.3x)=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-(-9.7x-1)-(13.3x+2.6)=0

We get rid of parentheses

3/8x+9.7x-13.3x+1-2.6=0

We multiply all the terms by the denominator


(9.7x)*8x-(13.3x)*8x+1*8x-(2.6)*8x+3=0

We add all the numbers together, and all the variables

(+9.7x)*8x-(+13.3x)*8x+1*8x-(2.6)*8x+3=0

We multiply parentheses

72x^2-104x^2+1*8x-20.8x+3=0

Wy multiply elements

72x^2-104x^2+8x-20.8x+3=0

We add all the numbers together, and all the variables

-32x^2-12.8x+3=0

a = -32; b = -12.8; c = +3;
Δ = b2-4ac
Δ = -12.82-4·(-32)·3
Δ = 547.84
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{-(-12.8)-\sqrt{547.84}}{2*-32}=\frac{12.8-\sqrt{547.84}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.8)+\sqrt{547.84}}{2*-32}=\frac{12.8+\sqrt{547.84}}{-64}
$