-7/4x+5=2/3x-9

Solution for -7/4x+5=2/3x-9 equation:

-7/4x+5=2/3x-9

We move all terms to the left:

-7/4x+5-(2/3x-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-9)!=0

x∈R


We get rid of parentheses

-7/4x-2/3x+9+5=0

We calculate fractions


(-21x)/12x^2+(-8x)/12x^2+9+5=0

We add all the numbers together, and all the variables

(-21x)/12x^2+(-8x)/12x^2+14=0

We multiply all the terms by the denominator


(-21x)+(-8x)+14*12x^2=0

Wy multiply elements

168x^2+(-21x)+(-8x)=0

We get rid of parentheses

168x^2-21x-8x=0

We add all the numbers together, and all the variables

168x^2-29x=0

a = 168; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·168·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*168}=\frac{0}{336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*168}=\frac{58}{336}
=29/168
$