2x(2x+10)=274

Solution for 2x(2x+10)=274 equation:

2x(2x+10)=274

We move all terms to the left:

2x(2x+10)-(274)=0

We multiply parentheses

4x^2+20x-274=0

a = 4; b = 20; c = -274;
Δ = b2-4ac
Δ = 202-4·4·(-274)
Δ = 4784
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:

$\sqrt{\Delta}=\sqrt{4784}=\sqrt{16*299}=\sqrt{16}*\sqrt{299}=4\sqrt{299}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{299}}{2*4}=\frac{-20-4\sqrt{299}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{299}}{2*4}=\frac{-20+4\sqrt{299}}{8}
$