4x(5x+10)=10x+5

Solution for 4x(5x+10)=10x+5 equation:

4x(5x+10)=10x+5

We move all terms to the left:

4x(5x+10)-(10x+5)=0

We multiply parentheses

20x^2+40x-(10x+5)=0

We get rid of parentheses

20x^2+40x-10x-5=0

We add all the numbers together, and all the variables

20x^2+30x-5=0

a = 20; b = 30; c = -5;
Δ = b2-4ac
Δ = 302-4·20·(-5)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{13}}{2*20}=\frac{-30-10\sqrt{13}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{13}}{2*20}=\frac{-30+10\sqrt{13}}{40}
$