(2x-6)(3x=5)

Solution for (2x-6)(3x=5) equation:

(2x-6)(3x=5)

We move all terms to the left:

(2x-6)(3x-(5))=0

We multiply parentheses ..

(+6x^2-10x-18x+30)=0

We get rid of parentheses

6x^2-10x-18x+30=0

We add all the numbers together, and all the variables

6x^2-28x+30=0

a = 6; b = -28; c = +30;
Δ = b2-4ac
Δ = -282-4·6·30
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8}{2*6}=\frac{20}{12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8}{2*6}=\frac{36}{12}
=3
$