5(2x+1)+2x(8+10x)=3

Solution for 5(2x+1)+2x(8+10x)=3 equation:

5(2x+1)+2x(8+10x)=3

We move all terms to the left:

5(2x+1)+2x(8+10x)-(3)=0

We add all the numbers together, and all the variables

5(2x+1)+2x(10x+8)-3=0

We multiply parentheses

20x^2+10x+16x+5-3=0

We add all the numbers together, and all the variables

20x^2+26x+2=0

a = 20; b = 26; c = +2;
Δ = b2-4ac
Δ = 262-4·20·2
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{129}}{2*20}=\frac{-26-2\sqrt{129}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{129}}{2*20}=\frac{-26+2\sqrt{129}}{40}
$