(1/5)(25x+15)-3=2x+9+3x

Solution for (1/5)(25x+15)-3=2x+9+3x equation:

(1/5)(25x+15)-3=2x+9+3x

We move all terms to the left:

(1/5)(25x+15)-3-(2x+9+3x)=0


Domain of the equation: 5)(25x+15)!=0

x∈R


We add all the numbers together, and all the variables

(+1/5)(25x+15)-(5x+9)-3=0

We get rid of parentheses

(+1/5)(25x+15)-5x-9-3=0

We multiply parentheses ..

(+25x^2+1/5*15)-5x-9-3=0

We multiply all the terms by the denominator


(+25x^2+1-5x*5*15)-9*5*15)-3*5*15)=0

We add all the numbers together, and all the variables

(+25x^2+1-5x*5*15)=0

We get rid of parentheses

25x^2-5x*5*15+1=0

Wy multiply elements

25x^2-375x*1+1=0

Wy multiply elements

25x^2-375x+1=0

a = 25; b = -375; c = +1;
Δ = b2-4ac
Δ = -3752-4·25·1
Δ = 140525
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:

$\sqrt{\Delta}=\sqrt{140525}=\sqrt{25*5621}=\sqrt{25}*\sqrt{5621}=5\sqrt{5621}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-375)-5\sqrt{5621}}{2*25}=\frac{375-5\sqrt{5621}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-375)+5\sqrt{5621}}{2*25}=\frac{375+5\sqrt{5621}}{50}
$