5x(2x+7)+x=(3x-5)

Solution for 5x(2x+7)+x=(3x-5) equation:

5x(2x+7)+x=(3x-5)

We move all terms to the left:

5x(2x+7)+x-((3x-5))=0

We add all the numbers together, and all the variables

x+5x(2x+7)-((3x-5))=0

We multiply parentheses

10x^2+x+35x-((3x-5))=0


We calculate terms in parentheses: -((3x-5)), so:

(3x-5)

We get rid of parentheses

3x-5

Back to the equation:

-(3x-5)


We add all the numbers together, and all the variables

10x^2+36x-(3x-5)=0

We get rid of parentheses

10x^2+36x-3x+5=0

We add all the numbers together, and all the variables

10x^2+33x+5=0

a = 10; b = 33; c = +5;
Δ = b2-4ac
Δ = 332-4·10·5
Δ = 889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{889}}{2*10}=\frac{-33-\sqrt{889}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{889}}{2*10}=\frac{-33+\sqrt{889}}{20}
$