3/5x+7=2x-10

Solution for 3/5x+7=2x-10 equation:

3/5x+7=2x-10

We move all terms to the left:

3/5x+7-(2x-10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-2x+10+7=0

We multiply all the terms by the denominator


-2x*5x+10*5x+7*5x+3=0

Wy multiply elements

-10x^2+50x+35x+3=0

We add all the numbers together, and all the variables

-10x^2+85x+3=0

a = -10; b = 85; c = +3;
Δ = b2-4ac
Δ = 852-4·(-10)·3
Δ = 7345
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{7345}}{2*-10}=\frac{-85-\sqrt{7345}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+\sqrt{7345}}{2*-10}=\frac{-85+\sqrt{7345}}{-20}
$