5x(2x+6)=(x+5)

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

5x(2x+6)=(x+5)

We move all terms to the left:

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

We multiply parentheses

10x^2+30x-((x+5))=0


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

(x+5)

We get rid of parentheses

x+5

Back to the equation:

-(x+5)


We get rid of parentheses

10x^2+30x-x-5=0

We add all the numbers together, and all the variables

10x^2+29x-5=0

a = 10; b = 29; c = -5;
Δ = b2-4ac
Δ = 292-4·10·(-5)
Δ = 1041
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{-(29)-\sqrt{1041}}{2*10}=\frac{-29-\sqrt{1041}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{1041}}{2*10}=\frac{-29+\sqrt{1041}}{20}
$