10x+10=1/2x-9

Solution for 10x+10=1/2x-9 equation:

10x+10=1/2x-9

We move all terms to the left:

10x+10-(1/2x-9)=0


Domain of the equation: 2x-9)!=0

x∈R


We get rid of parentheses

10x-1/2x+9+10=0

We multiply all the terms by the denominator


10x*2x+9*2x+10*2x-1=0

Wy multiply elements

20x^2+18x+20x-1=0

We add all the numbers together, and all the variables

20x^2+38x-1=0

a = 20; b = 38; c = -1;
Δ = b2-4ac
Δ = 382-4·20·(-1)
Δ = 1524
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:

$\sqrt{\Delta}=\sqrt{1524}=\sqrt{4*381}=\sqrt{4}*\sqrt{381}=2\sqrt{381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{381}}{2*20}=\frac{-38-2\sqrt{381}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{381}}{2*20}=\frac{-38+2\sqrt{381}}{40}
$