2x(10x+8)=3(x+1)

Solution for 2x(10x+8)=3(x+1) equation:

2x(10x+8)=3(x+1)

We move all terms to the left:

2x(10x+8)-(3(x+1))=0

We multiply parentheses

20x^2+16x-(3(x+1))=0


We calculate terms in parentheses: -(3(x+1)), so:

3(x+1)

We multiply parentheses

3x+3

Back to the equation:

-(3x+3)


We get rid of parentheses

20x^2+16x-3x-3=0

We add all the numbers together, and all the variables

20x^2+13x-3=0

a = 20; b = 13; c = -3;
Δ = b2-4ac
Δ = 132-4·20·(-3)
Δ = 409
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{-(13)-\sqrt{409}}{2*20}=\frac{-13-\sqrt{409}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{409}}{2*20}=\frac{-13+\sqrt{409}}{40}
$