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-(-16x+37)+17=0

We get rid of parentheses

3/4x+16x-37+17=0

We multiply all the terms by the denominator


16x*4x-37*4x+17*4x+3=0

Wy multiply elements

64x^2-148x+68x+3=0

We add all the numbers together, and all the variables

64x^2-80x+3=0

a = 64; b = -80; c = +3;
Δ = b2-4ac
Δ = -802-4·64·3
Δ = 5632
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:

$\sqrt{\Delta}=\sqrt{5632}=\sqrt{256*22}=\sqrt{256}*\sqrt{22}=16\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{22}}{2*64}=\frac{80-16\sqrt{22}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{22}}{2*64}=\frac{80+16\sqrt{22}}{128}
$