5x(x+2)=+4+34

Solution for 5x(x+2)=+4+34 equation:

5x(x+2)=+4+34

We move all terms to the left:

5x(x+2)-(+4+34)=0

We add all the numbers together, and all the variables

5x(x+2)-38=0

We multiply parentheses

5x^2+10x-38=0

a = 5; b = 10; c = -38;
Δ = b2-4ac
Δ = 102-4·5·(-38)
Δ = 860
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:

$\sqrt{\Delta}=\sqrt{860}=\sqrt{4*215}=\sqrt{4}*\sqrt{215}=2\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{215}}{2*5}=\frac{-10-2\sqrt{215}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{215}}{2*5}=\frac{-10+2\sqrt{215}}{10}
$