3/4x+17=-9x+7x+37

Solution for 3/4x+17=-9x+7x+37 equation:

3/4x+17=-9x+7x+37

We move all terms to the left:

3/4x+17-(-9x+7x+37)=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-(-2x+37)+17=0

We get rid of parentheses

3/4x+2x-37+17=0

We multiply all the terms by the denominator


2x*4x-37*4x+17*4x+3=0

Wy multiply elements

8x^2-148x+68x+3=0

We add all the numbers together, and all the variables

8x^2-80x+3=0

a = 8; b = -80; c = +3;
Δ = b2-4ac
Δ = -802-4·8·3
Δ = 6304
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:

$\sqrt{\Delta}=\sqrt{6304}=\sqrt{16*394}=\sqrt{16}*\sqrt{394}=4\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{394}}{2*8}=\frac{80-4\sqrt{394}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{394}}{2*8}=\frac{80+4\sqrt{394}}{16}
$