(2x-14)(15-3x)=0

Solution for (2x-14)(15-3x)=0 equation:

(2x-14)(15-3x)=0

We add all the numbers together, and all the variables

(2x-14)(-3x+15)=0

We multiply parentheses ..

(-6x^2+30x+42x-210)=0

We get rid of parentheses

-6x^2+30x+42x-210=0

We add all the numbers together, and all the variables

-6x^2+72x-210=0

a = -6; b = 72; c = -210;
Δ = b2-4ac
Δ = 722-4·(-6)·(-210)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12}{2*-6}=\frac{-84}{-12}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12}{2*-6}=\frac{-60}{-12}
=+5
$