(2x-3)(x+5)/x-7=0

Solution for (2x-3)(x+5)/x-7=0 equation:

(2x-3)(x+5)/x-7=0


Domain of the equation: x!=0

x∈R


We multiply parentheses ..

(+2x^2+10x-3x-15)/x-7=0

We multiply all the terms by the denominator


(+2x^2+10x-3x-15)-7*x=0

We add all the numbers together, and all the variables

(+2x^2+10x-3x-15)-7x=0

We get rid of parentheses

2x^2+10x-3x-7x-15=0

We add all the numbers together, and all the variables

2x^2-15=0

a = 2; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·2·(-15)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*2}=\frac{0-2\sqrt{30}}{4}
=-\frac{2\sqrt{30}}{4}
=-\frac{\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*2}=\frac{0+2\sqrt{30}}{4}
=\frac{2\sqrt{30}}{4}
=\frac{\sqrt{30}}{2}
$