11+6x-14=(3/5)(15x-5)

Solution for 11+6x-14=(3/5)(15x-5) equation:

11+6x-14=(3/5)(15x-5)

We move all terms to the left:

11+6x-14-((3/5)(15x-5))=0


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

x∈R


We add all the numbers together, and all the variables

6x-((+3/5)(15x-5))+11-14=0

We add all the numbers together, and all the variables

6x-((+3/5)(15x-5))-3=0

We multiply parentheses ..

-((+45x^2+3/5*-5))+6x-3=0

We multiply all the terms by the denominator


-((+45x^2+3+6x*5*-5))-3*5*-5))=0


We calculate terms in parentheses: -((+45x^2+3+6x*5*-5)), so:

(+45x^2+3+6x*5*-5)

We get rid of parentheses

45x^2+6x*5*+3-5

We add all the numbers together, and all the variables

45x^2+6x*5*-2

Wy multiply elements

45x^2+30x^2-2

We add all the numbers together, and all the variables

75x^2-2

Back to the equation:

-(75x^2-2)


We add all the numbers together, and all the variables

-(75x^2-2)=0

We get rid of parentheses

-75x^2+2=0

a = -75; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-75)·2
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-75}=\frac{0-10\sqrt{6}}{-150}
=-\frac{10\sqrt{6}}{-150}
=-\frac{\sqrt{6}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-75}=\frac{0+10\sqrt{6}}{-150}
=\frac{10\sqrt{6}}{-150}
=\frac{\sqrt{6}}{-15}
$