10x+3/4x-8=5x+2x-4

Solution for 10x+3/4x-8=5x+2x-4 equation:

10x+3/4x-8=5x+2x-4

We move all terms to the left:

10x+3/4x-8-(5x+2x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

10x+3/4x-(7x-4)-8=0

We get rid of parentheses

10x+3/4x-7x+4-8=0

We multiply all the terms by the denominator


10x*4x-7x*4x+4*4x-8*4x+3=0

Wy multiply elements

40x^2-28x^2+16x-32x+3=0

We add all the numbers together, and all the variables

12x^2-16x+3=0

a = 12; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·12·3
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*12}=\frac{16-4\sqrt{7}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*12}=\frac{16+4\sqrt{7}}{24}
$