3/4x-10=3+x

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

3/4x-10=3+x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/4x-x-3-10=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-12x-40x+3=0

We add all the numbers together, and all the variables

-4x^2-52x+3=0

a = -4; b = -52; c = +3;
Δ = b2-4ac
Δ = -522-4·(-4)·3
Δ = 2752
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:

$\sqrt{\Delta}=\sqrt{2752}=\sqrt{64*43}=\sqrt{64}*\sqrt{43}=8\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-8\sqrt{43}}{2*-4}=\frac{52-8\sqrt{43}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+8\sqrt{43}}{2*-4}=\frac{52+8\sqrt{43}}{-8}
$