1.4x-3=3/8x+4

Solution for 1.4x-3=3/8x+4 equation:

1.4x-3=3/8x+4

We move all terms to the left:

1.4x-3-(3/8x+4)=0


Domain of the equation: 8x+4)!=0

x∈R


We get rid of parentheses

1.4x-3/8x-4-3=0

We multiply all the terms by the denominator


(1.4x)*8x-4*8x-3*8x-3=0

We add all the numbers together, and all the variables

(+1.4x)*8x-4*8x-3*8x-3=0

We multiply parentheses

8x^2-4*8x-3*8x-3=0

Wy multiply elements

8x^2-32x-24x-3=0

We add all the numbers together, and all the variables

8x^2-56x-3=0

a = 8; b = -56; c = -3;
Δ = b2-4ac
Δ = -562-4·8·(-3)
Δ = 3232
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:

$\sqrt{\Delta}=\sqrt{3232}=\sqrt{16*202}=\sqrt{16}*\sqrt{202}=4\sqrt{202}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{202}}{2*8}=\frac{56-4\sqrt{202}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{202}}{2*8}=\frac{56+4\sqrt{202}}{16}
$