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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+20x^2-8x+5x-2)=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{-10}{40}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*20}=\frac{16}{40}
=2/5
$