(2x+50)(2x+20)-(50)(20)=456

Solution for (2x+50)(2x+20)-(50)(20)=456 equation:

(2x+50)(2x+20)-(50)(20)=456

We move all terms to the left:

(2x+50)(2x+20)-(50)(20)-(456)=0

We add all the numbers together, and all the variables

(2x+50)(2x+20)-5476=0

We multiply parentheses ..

(+4x^2+40x+100x+1000)-5476=0

We get rid of parentheses

4x^2+40x+100x+1000-5476=0

We add all the numbers together, and all the variables

4x^2+140x-4476=0

a = 4; b = 140; c = -4476;
Δ = b2-4ac
Δ = 1402-4·4·(-4476)
Δ = 91216
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:

$\sqrt{\Delta}=\sqrt{91216}=\sqrt{16*5701}=\sqrt{16}*\sqrt{5701}=4\sqrt{5701}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-4\sqrt{5701}}{2*4}=\frac{-140-4\sqrt{5701}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+4\sqrt{5701}}{2*4}=\frac{-140+4\sqrt{5701}}{8}
$