5x(x+5)=7

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

5x(x+5)=7

We move all terms to the left:

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

We multiply parentheses

5x^2+25x-7=0

a = 5; b = 25; c = -7;
Δ = b2-4ac
Δ = 252-4·5·(-7)
Δ = 765
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:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-3\sqrt{85}}{2*5}=\frac{-25-3\sqrt{85}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+3\sqrt{85}}{2*5}=\frac{-25+3\sqrt{85}}{10}
$