8x+2=20x2+5x

Solution for 8x+2=20x2+5x equation:

8x+2=20x^2+5x

We move all terms to the left:

8x+2-(20x^2+5x)=0

We get rid of parentheses

-20x^2+8x-5x+2=0

We add all the numbers together, and all the variables

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

a = -20; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-20)·2
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*-20}=\frac{-16}{-40}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*-20}=\frac{10}{-40}
=-1/4
$