3x-10=2/5x+18

Solution for 3x-10=2/5x+18 equation:

3x-10=2/5x+18

We move all terms to the left:

3x-10-(2/5x+18)=0


Domain of the equation: 5x+18)!=0

x∈R


We get rid of parentheses

3x-2/5x-18-10=0

We multiply all the terms by the denominator


3x*5x-18*5x-10*5x-2=0

Wy multiply elements

15x^2-90x-50x-2=0

We add all the numbers together, and all the variables

15x^2-140x-2=0

a = 15; b = -140; c = -2;
Δ = b2-4ac
Δ = -1402-4·15·(-2)
Δ = 19720
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:

$\sqrt{\Delta}=\sqrt{19720}=\sqrt{4*4930}=\sqrt{4}*\sqrt{4930}=2\sqrt{4930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4930}}{2*15}=\frac{140-2\sqrt{4930}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4930}}{2*15}=\frac{140+2\sqrt{4930}}{30}
$