4x(5x+5)=101

Solution for 4x(5x+5)=101 equation:

4x(5x+5)=101

We move all terms to the left:

4x(5x+5)-(101)=0

We multiply parentheses

20x^2+20x-101=0

a = 20; b = 20; c = -101;
Δ = b2-4ac
Δ = 202-4·20·(-101)
Δ = 8480
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:

$\sqrt{\Delta}=\sqrt{8480}=\sqrt{16*530}=\sqrt{16}*\sqrt{530}=4\sqrt{530}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{530}}{2*20}=\frac{-20-4\sqrt{530}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{530}}{2*20}=\frac{-20+4\sqrt{530}}{40}
$