5x(2x-1)+x+17=5x+6(x+2)

Solution for 5x(2x-1)+x+17=5x+6(x+2) equation:

5x(2x-1)+x+17=5x+6(x+2)

We move all terms to the left:

5x(2x-1)+x+17-(5x+6(x+2))=0

We add all the numbers together, and all the variables

x+5x(2x-1)-(5x+6(x+2))+17=0

We multiply parentheses

10x^2+x-5x-(5x+6(x+2))+17=0


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

5x+6(x+2)

We multiply parentheses

5x+6x+12

We add all the numbers together, and all the variables

11x+12

Back to the equation:

-(11x+12)


We add all the numbers together, and all the variables

10x^2-4x-(11x+12)+17=0

We get rid of parentheses

10x^2-4x-11x-12+17=0

We add all the numbers together, and all the variables

10x^2-15x+5=0

a = 10; b = -15; c = +5;
Δ = b2-4ac
Δ = -152-4·10·5
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5}{2*10}=\frac{10}{20}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5}{2*10}=\frac{20}{20}
=1
$