4(x+5)(5x+2)=100x^2+80x+16

Solution for 4(x+5)(5x+2)=100x^2+80x+16 equation:

4(x+5)(5x+2)=100x^2+80x+16

We move all terms to the left:

4(x+5)(5x+2)-(100x^2+80x+16)=0

We get rid of parentheses

-100x^2+4(x+5)(5x+2)-80x-16=0

We multiply parentheses ..

-100x^2+4(+5x^2+2x+25x+10)-80x-16=0

We multiply parentheses

-100x^2+20x^2+8x+100x-80x+40-16=0

We add all the numbers together, and all the variables

-80x^2+28x+24=0

a = -80; b = 28; c = +24;
Δ = b2-4ac
Δ = 282-4·(-80)·24
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-92}{2*-80}=\frac{-120}{-160}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+92}{2*-80}=\frac{64}{-160}
=-2/5
$