5x(x+6)=7

Solution for 5x(x+6)=7 equation:

5x(x+6)=7

We move all terms to the left:

5x(x+6)-(7)=0

We multiply parentheses

5x^2+30x-7=0

a = 5; b = 30; c = -7;
Δ = b2-4ac
Δ = 302-4·5·(-7)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{65}}{2*5}=\frac{-30-4\sqrt{65}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{65}}{2*5}=\frac{-30+4\sqrt{65}}{10}
$