10.5-x+3/4x=5

Solution for 10.5-x+3/4x=5 equation:

10.5-x+3/4x=5

We move all terms to the left:

10.5-x+3/4x-(5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/4x+5.5=0

We multiply all the terms by the denominator


-1x*4x+(5.5)*4x+3=0

We multiply parentheses

-1x*4x+22x+3=0

Wy multiply elements

-4x^2+22x+3=0

a = -4; b = 22; c = +3;
Δ = b2-4ac
Δ = 222-4·(-4)·3
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{133}}{2*-4}=\frac{-22-2\sqrt{133}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{133}}{2*-4}=\frac{-22+2\sqrt{133}}{-8}
$