3x-10=1/2*4x-10

Solution for 3x-10=1/2*4x-10 equation:

3x-10=1/2*4x-10

We move all terms to the left:

3x-10-(1/2*4x-10)=0


Domain of the equation: 2*4x-10)!=0

x∈R


We get rid of parentheses

3x-1/2*4x+10-10=0

We multiply all the terms by the denominator


3x*2*4x+10*2*4x-10*2*4x-1=0

Wy multiply elements

24x^2*4+80x*4-80x*4-1=0

Wy multiply elements

96x^2+320x-320x-1=0

We add all the numbers together, and all the variables

96x^2-1=0

a = 96; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·96·(-1)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*96}=\frac{0-8\sqrt{6}}{192}
=-\frac{8\sqrt{6}}{192}
=-\frac{\sqrt{6}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*96}=\frac{0+8\sqrt{6}}{192}
=\frac{8\sqrt{6}}{192}
=\frac{\sqrt{6}}{24}
$