2x+17=-3/4x-6

Solution for 2x+17=-3/4x-6 equation:

2x+17=-3/4x-6

We move all terms to the left:

2x+17-(-3/4x-6)=0


Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

2x+3/4x+6+17=0

We multiply all the terms by the denominator


2x*4x+6*4x+17*4x+3=0

Wy multiply elements

8x^2+24x+68x+3=0

We add all the numbers together, and all the variables

8x^2+92x+3=0

a = 8; b = 92; c = +3;
Δ = b2-4ac
Δ = 922-4·8·3
Δ = 8368
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:

$\sqrt{\Delta}=\sqrt{8368}=\sqrt{16*523}=\sqrt{16}*\sqrt{523}=4\sqrt{523}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-4\sqrt{523}}{2*8}=\frac{-92-4\sqrt{523}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+4\sqrt{523}}{2*8}=\frac{-92+4\sqrt{523}}{16}
$