2x-3=13/4x+10-1.25x

Solution for 2x-3=13/4x+10-1.25x equation:

2x-3=13/4x+10-1.25x

We move all terms to the left:

2x-3-(13/4x+10-1.25x)=0


Domain of the equation: 4x+10-1.25x)!=0

We move all terms containing x to the left, all other terms to the right

4x-1.25x)!=-10

x∈R


We add all the numbers together, and all the variables

2x-(-1.25x+13/4x+10)-3=0

We get rid of parentheses

2x+1.25x-13/4x-10-3=0

We multiply all the terms by the denominator


2x*4x+(1.25x)*4x-10*4x-3*4x-13=0

We add all the numbers together, and all the variables

2x*4x+(+1.25x)*4x-10*4x-3*4x-13=0

We multiply parentheses

4x^2+2x*4x-10*4x-3*4x-13=0

Wy multiply elements

4x^2+8x^2-40x-12x-13=0

We add all the numbers together, and all the variables

12x^2-52x-13=0

a = 12; b = -52; c = -13;
Δ = b2-4ac
Δ = -522-4·12·(-13)
Δ = 3328
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:

$\sqrt{\Delta}=\sqrt{3328}=\sqrt{256*13}=\sqrt{256}*\sqrt{13}=16\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-16\sqrt{13}}{2*12}=\frac{52-16\sqrt{13}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+16\sqrt{13}}{2*12}=\frac{52+16\sqrt{13}}{24}
$