(2x+10)(x+10)2=84

Solution for (2x+10)(x+10)2=84 equation:

(2x+10)(x+10)2=84

We move all terms to the left:

(2x+10)(x+10)2-(84)=0

We multiply parentheses ..

(+2x^2+20x+10x+100)2-84=0

We multiply parentheses

4x^2+40x+20x+200-84=0

We add all the numbers together, and all the variables

4x^2+60x+116=0

a = 4; b = 60; c = +116;
Δ = b2-4ac
Δ = 602-4·4·116
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{109}}{2*4}=\frac{-60-4\sqrt{109}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{109}}{2*4}=\frac{-60+4\sqrt{109}}{8}
$