15x+9=1/2x-20

Solution for 15x+9=1/2x-20 equation:

15x+9=1/2x-20

We move all terms to the left:

15x+9-(1/2x-20)=0


Domain of the equation: 2x-20)!=0

x∈R


We get rid of parentheses

15x-1/2x+20+9=0

We multiply all the terms by the denominator


15x*2x+20*2x+9*2x-1=0

Wy multiply elements

30x^2+40x+18x-1=0

We add all the numbers together, and all the variables

30x^2+58x-1=0

a = 30; b = 58; c = -1;
Δ = b2-4ac
Δ = 582-4·30·(-1)
Δ = 3484
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:

$\sqrt{\Delta}=\sqrt{3484}=\sqrt{4*871}=\sqrt{4}*\sqrt{871}=2\sqrt{871}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{871}}{2*30}=\frac{-58-2\sqrt{871}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{871}}{2*30}=\frac{-58+2\sqrt{871}}{60}
$