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

Solution for (2x+5)(6-5x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-10x^2+12x-25x+30)=0

We get rid of parentheses

-10x^2+12x-25x+30=0

We add all the numbers together, and all the variables

-10x^2-13x+30=0

a = -10; b = -13; c = +30;
Δ = b2-4ac
Δ = -132-4·(-10)·30
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-37}{2*-10}=\frac{-24}{-20}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+37}{2*-10}=\frac{50}{-20}
=-2+1/2
$