3x(x-5)=5x+7

Solution for 3x(x-5)=5x+7 equation:

3x(x-5)=5x+7

We move all terms to the left:

3x(x-5)-(5x+7)=0

We multiply parentheses

3x^2-15x-(5x+7)=0

We get rid of parentheses

3x^2-15x-5x-7=0

We add all the numbers together, and all the variables

3x^2-20x-7=0

a = 3; b = -20; c = -7;
Δ = b2-4ac
Δ = -202-4·3·(-7)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-22}{2*3}=\frac{-2}{6}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+22}{2*3}=\frac{42}{6}
=7
$