7/5x+8=3x-9

Solution for 7/5x+8=3x-9 equation:

7/5x+8=3x-9

We move all terms to the left:

7/5x+8-(3x-9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

7/5x-3x+9+8=0

We multiply all the terms by the denominator


-3x*5x+9*5x+8*5x+7=0

Wy multiply elements

-15x^2+45x+40x+7=0

We add all the numbers together, and all the variables

-15x^2+85x+7=0

a = -15; b = 85; c = +7;
Δ = b2-4ac
Δ = 852-4·(-15)·7
Δ = 7645
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-\sqrt{7645}}{2*-15}=\frac{-85-\sqrt{7645}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+\sqrt{7645}}{2*-15}=\frac{-85+\sqrt{7645}}{-30}
$