5x(5x+2)-4(x+3)=50

Solution for 5x(5x+2)-4(x+3)=50 equation:

5x(5x+2)-4(x+3)=50

We move all terms to the left:

5x(5x+2)-4(x+3)-(50)=0

We multiply parentheses

25x^2+10x-4x-12-50=0

We add all the numbers together, and all the variables

25x^2+6x-62=0

a = 25; b = 6; c = -62;
Δ = b2-4ac
Δ = 62-4·25·(-62)
Δ = 6236
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:

$\sqrt{\Delta}=\sqrt{6236}=\sqrt{4*1559}=\sqrt{4}*\sqrt{1559}=2\sqrt{1559}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1559}}{2*25}=\frac{-6-2\sqrt{1559}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1559}}{2*25}=\frac{-6+2\sqrt{1559}}{50}
$