4(2x+6)=5x(x+5)+2

Solution for 4(2x+6)=5x(x+5)+2 equation:

4(2x+6)=5x(x+5)+2

We move all terms to the left:

4(2x+6)-(5x(x+5)+2)=0

We multiply parentheses

8x-(5x(x+5)+2)+24=0


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

5x(x+5)+2

We multiply parentheses

5x^2+25x+2

Back to the equation:

-(5x^2+25x+2)


We get rid of parentheses

-5x^2+8x-25x-2+24=0

We add all the numbers together, and all the variables

-5x^2-17x+22=0

a = -5; b = -17; c = +22;
Δ = b2-4ac
Δ = -172-4·(-5)·22
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-27}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+27}{2*-5}=\frac{44}{-10}
=-4+2/5
$