(x+3)(x-3)=60/40

Solution for (x+3)(x-3)=60/40 equation:

(x+3)(x-3)=60/40

We move all terms to the left:

(x+3)(x-3)-(60/40)=0

We add all the numbers together, and all the variables

(x+3)(x-3)-(+60/40)=0

We use the square of the difference formula

x^2-9-(+60/40)=0

We get rid of parentheses

x^2-9-60/40=0

We multiply all the terms by the denominator


x^2*40-60-9*40=0

We add all the numbers together, and all the variables

x^2*40-420=0

Wy multiply elements

40x^2-420=0

a = 40; b = 0; c = -420;
Δ = b2-4ac
Δ = 02-4·40·(-420)
Δ = 67200
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:

$\sqrt{\Delta}=\sqrt{67200}=\sqrt{1600*42}=\sqrt{1600}*\sqrt{42}=40\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{42}}{2*40}=\frac{0-40\sqrt{42}}{80}
=-\frac{40\sqrt{42}}{80}
=-\frac{\sqrt{42}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{42}}{2*40}=\frac{0+40\sqrt{42}}{80}
=\frac{40\sqrt{42}}{80}
=\frac{\sqrt{42}}{2}
$