-3/4x+9=5/2x-17

Solution for -3/4x+9=5/2x-17 equation:

-3/4x+9=5/2x-17

We move all terms to the left:

-3/4x+9-(5/2x-17)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-17)!=0

x∈R


We get rid of parentheses

-3/4x-5/2x+17+9=0

We calculate fractions


(-6x)/8x^2+(-20x)/8x^2+17+9=0

We add all the numbers together, and all the variables

(-6x)/8x^2+(-20x)/8x^2+26=0

We multiply all the terms by the denominator


(-6x)+(-20x)+26*8x^2=0

Wy multiply elements

208x^2+(-6x)+(-20x)=0

We get rid of parentheses

208x^2-6x-20x=0

We add all the numbers together, and all the variables

208x^2-26x=0

a = 208; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·208·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*208}=\frac{0}{416}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*208}=\frac{52}{416}
=1/8
$