10x-3/4x=2

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

10x-3/4x=2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

40x^2-8x-3=0

a = 40; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·40·(-3)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{34}}{2*40}=\frac{8-4\sqrt{34}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{34}}{2*40}=\frac{8+4\sqrt{34}}{80}
$