X-3/8x=2x-11

Solution for X-3/8x=2x-11 equation:

X-3/8X=2X-11

We move all terms to the left:

X-3/8X-(2X-11)=0


Domain of the equation: 8X!=0

X!=0/8

X!=0

X∈R


We get rid of parentheses

X-3/8X-2X+11=0

We multiply all the terms by the denominator


X*8X-2X*8X+11*8X-3=0

Wy multiply elements

8X^2-16X^2+88X-3=0

We add all the numbers together, and all the variables

-8X^2+88X-3=0

a = -8; b = 88; c = -3;
Δ = b2-4ac
Δ = 882-4·(-8)·(-3)
Δ = 7648
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:

$\sqrt{\Delta}=\sqrt{7648}=\sqrt{16*478}=\sqrt{16}*\sqrt{478}=4\sqrt{478}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-4\sqrt{478}}{2*-8}=\frac{-88-4\sqrt{478}}{-16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+4\sqrt{478}}{2*-8}=\frac{-88+4\sqrt{478}}{-16}
$