x(2x+7)=30

Solution for x(2x+7)=30 equation:

x(2x+7)=30

We move all terms to the left:

x(2x+7)-(30)=0

We multiply parentheses

2x^2+7x-30=0

a = 2; b = 7; c = -30;
Δ = b2-4ac
Δ = 72-4·2·(-30)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*2}=\frac{10}{4}
=2+1/2
$