625-x+20=3/5x+17

Solution for 625-x+20=3/5x+17 equation:

625-x+20=3/5x+17

We move all terms to the left:

625-x+20-(3/5x+17)=0


Domain of the equation: 5x+17)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(3/5x+17)+645=0

We get rid of parentheses

-1x-3/5x-17+645=0

We multiply all the terms by the denominator


-1x*5x-17*5x+645*5x-3=0

Wy multiply elements

-5x^2-85x+3225x-3=0

We add all the numbers together, and all the variables

-5x^2+3140x-3=0

a = -5; b = 3140; c = -3;
Δ = b2-4ac
Δ = 31402-4·(-5)·(-3)
Δ = 9859540
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:

$\sqrt{\Delta}=\sqrt{9859540}=\sqrt{4*2464885}=\sqrt{4}*\sqrt{2464885}=2\sqrt{2464885}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3140)-2\sqrt{2464885}}{2*-5}=\frac{-3140-2\sqrt{2464885}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3140)+2\sqrt{2464885}}{2*-5}=\frac{-3140+2\sqrt{2464885}}{-10}
$