5x(x-2)=7

Solution for 5x(x-2)=7 equation:

5x(x-2)=7

We move all terms to the left:

5x(x-2)-(7)=0

We multiply parentheses

5x^2-10x-7=0

a = 5; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·5·(-7)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{15}}{2*5}=\frac{10-4\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{15}}{2*5}=\frac{10+4\sqrt{15}}{10}
$