3/4x+7=22+x

Solution for 3/4x+7=22+x equation:

3/4x+7=22+x

We move all terms to the left:

3/4x+7-(22+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+22)+7=0

We get rid of parentheses

3/4x-x-22+7=0

We multiply all the terms by the denominator


-x*4x-22*4x+7*4x+3=0

Wy multiply elements

-4x^2-88x+28x+3=0

We add all the numbers together, and all the variables

-4x^2-60x+3=0

a = -4; b = -60; c = +3;
Δ = b2-4ac
Δ = -602-4·(-4)·3
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-8\sqrt{57}}{2*-4}=\frac{60-8\sqrt{57}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+8\sqrt{57}}{2*-4}=\frac{60+8\sqrt{57}}{-8}
$