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

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

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

We move all terms to the left:

(1/5)(25x+15)-3-(2x+9+3)=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)-(2x+12)-3=0

We get rid of parentheses

(+1/5)(25x+15)-2x-12-3=0

We multiply parentheses ..

(+25x^2+1/5*15)-2x-12-3=0

We multiply all the terms by the denominator


(+25x^2+1-2x*5*15)-12*5*15)-3*5*15)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

Wy multiply elements

25x^2-150x*1+1=0

Wy multiply elements

25x^2-150x+1=0

a = 25; b = -150; c = +1;
Δ = b2-4ac
Δ = -1502-4·25·1
Δ = 22400
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:

$\sqrt{\Delta}=\sqrt{22400}=\sqrt{1600*14}=\sqrt{1600}*\sqrt{14}=40\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-40\sqrt{14}}{2*25}=\frac{150-40\sqrt{14}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+40\sqrt{14}}{2*25}=\frac{150+40\sqrt{14}}{50}
$