x(2x+7)=774

Solution for x(2x+7)=774 equation:

x(2x+7)=774

We move all terms to the left:

x(2x+7)-(774)=0

We multiply parentheses

2x^2+7x-774=0

a = 2; b = 7; c = -774;
Δ = b2-4ac
Δ = 72-4·2·(-774)
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-79}{2*2}=\frac{-86}{4}
=-21+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+79}{2*2}=\frac{72}{4}
=18
$