3/4x+37=2x-13

Solution for 3/4x+37=2x-13 equation:

3/4x+37=2x-13

We move all terms to the left:

3/4x+37-(2x-13)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-2x+13+37=0

We multiply all the terms by the denominator


-2x*4x+13*4x+37*4x+3=0

Wy multiply elements

-8x^2+52x+148x+3=0

We add all the numbers together, and all the variables

-8x^2+200x+3=0

a = -8; b = 200; c = +3;
Δ = b2-4ac
Δ = 2002-4·(-8)·3
Δ = 40096
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:

$\sqrt{\Delta}=\sqrt{40096}=\sqrt{16*2506}=\sqrt{16}*\sqrt{2506}=4\sqrt{2506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-4\sqrt{2506}}{2*-8}=\frac{-200-4\sqrt{2506}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+4\sqrt{2506}}{2*-8}=\frac{-200+4\sqrt{2506}}{-16}
$