3/4x+7=x+13

Solution for 3/4x+7=x+13 equation:

3/4x+7=x+13

We move all terms to the left:

3/4x+7-(x+13)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-x-13+7=0

We multiply all the terms by the denominator


-x*4x-13*4x+7*4x+3=0

Wy multiply elements

-4x^2-52x+28x+3=0

We add all the numbers together, and all the variables

-4x^2-24x+3=0

a = -4; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·(-4)·3
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*-4}=\frac{24-4\sqrt{39}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*-4}=\frac{24+4\sqrt{39}}{-8}
$