2x(25+x)=3(2x-46)

Solution for 2x(25+x)=3(2x-46) equation:

2x(25+x)=3(2x-46)

We move all terms to the left:

2x(25+x)-(3(2x-46))=0

We add all the numbers together, and all the variables

2x(x+25)-(3(2x-46))=0

We multiply parentheses

2x^2+50x-(3(2x-46))=0


We calculate terms in parentheses: -(3(2x-46)), so:

3(2x-46)

We multiply parentheses

6x-138

Back to the equation:

-(6x-138)


We get rid of parentheses

2x^2+50x-6x+138=0

We add all the numbers together, and all the variables

2x^2+44x+138=0

a = 2; b = 44; c = +138;
Δ = b2-4ac
Δ = 442-4·2·138
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-8\sqrt{13}}{2*2}=\frac{-44-8\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+8\sqrt{13}}{2*2}=\frac{-44+8\sqrt{13}}{4}
$