3/5x-10=8x-10

Solution for 3/5x-10=8x-10 equation:

3/5x-10=8x-10

We move all terms to the left:

3/5x-10-(8x-10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-8x+10-10=0

We multiply all the terms by the denominator


-8x*5x+10*5x-10*5x+3=0

Wy multiply elements

-40x^2+50x-50x+3=0

We add all the numbers together, and all the variables

-40x^2+3=0

a = -40; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-40)·3
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-40}=\frac{0-4\sqrt{30}}{-80}
=-\frac{4\sqrt{30}}{-80}
=-\frac{\sqrt{30}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-40}=\frac{0+4\sqrt{30}}{-80}
=\frac{4\sqrt{30}}{-80}
=\frac{\sqrt{30}}{-20}
$