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

Solution for (3x+5)(5x-6)=0 equation:

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

We multiply parentheses ..

(+15x^2-18x+25x-30)=0

We get rid of parentheses

15x^2-18x+25x-30=0

We add all the numbers together, and all the variables

15x^2+7x-30=0

a = 15; b = 7; c = -30;
Δ = b2-4ac
Δ = 72-4·15·(-30)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-43}{2*15}=\frac{-50}{30}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+43}{2*15}=\frac{36}{30}
=1+1/5
$