7+x=(3/5)(49+x)

Solution for 7+x=(3/5)(49+x) equation:

7+x=(3/5)(49+x)

We move all terms to the left:

7+x-((3/5)(49+x))=0


Domain of the equation: 5)(49+x))!=0

x∈R


We add all the numbers together, and all the variables

x-((+3/5)(x+49))+7=0

We multiply parentheses ..

-((+3x^2+3/5*49))+x+7=0

We multiply all the terms by the denominator


-((+3x^2+3+x*5*49))+7*5*49))=0


We calculate terms in parentheses: -((+3x^2+3+x*5*49)), so:

(+3x^2+3+x*5*49)

We get rid of parentheses

3x^2+x*5*49+3

Wy multiply elements

3x^2+245x*4+3

Wy multiply elements

3x^2+980x+3

Back to the equation:

-(3x^2+980x+3)


We add all the numbers together, and all the variables

-(3x^2+980x+3)=0

We get rid of parentheses

-3x^2-980x-3=0

a = -3; b = -980; c = -3;
Δ = b2-4ac
Δ = -9802-4·(-3)·(-3)
Δ = 960364
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:

$\sqrt{\Delta}=\sqrt{960364}=\sqrt{4*240091}=\sqrt{4}*\sqrt{240091}=2\sqrt{240091}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-980)-2\sqrt{240091}}{2*-3}=\frac{980-2\sqrt{240091}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-980)+2\sqrt{240091}}{2*-3}=\frac{980+2\sqrt{240091}}{-6}
$