(5x+2)=(5x+6)(4x-1)

Solution for (5x+2)=(5x+6)(4x-1) equation:

(5x+2)=(5x+6)(4x-1)

We move all terms to the left:

(5x+2)-((5x+6)(4x-1))=0

We get rid of parentheses

5x-((5x+6)(4x-1))+2=0

We multiply parentheses ..

-((+20x^2-5x+24x-6))+5x+2=0


We calculate terms in parentheses: -((+20x^2-5x+24x-6)), so:

(+20x^2-5x+24x-6)

We get rid of parentheses

20x^2-5x+24x-6

We add all the numbers together, and all the variables

20x^2+19x-6

Back to the equation:

-(20x^2+19x-6)


We add all the numbers together, and all the variables

5x-(20x^2+19x-6)+2=0

We get rid of parentheses

-20x^2+5x-19x+6+2=0

We add all the numbers together, and all the variables

-20x^2-14x+8=0

a = -20; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·(-20)·8
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{209}}{2*-20}=\frac{14-2\sqrt{209}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{209}}{2*-20}=\frac{14+2\sqrt{209}}{-40}
$