3/4x+x-2=8

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

3/4x+x-2=8

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/4x-10=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-40x+3=0

a = 4; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·4·3
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{97}}{2*4}=\frac{40-4\sqrt{97}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{97}}{2*4}=\frac{40+4\sqrt{97}}{8}
$