(2x+7)(5x-15)=0

Solution for (2x+7)(5x-15)=0 equation:

(2x+7)(5x-15)=0

We multiply parentheses ..

(+10x^2-30x+35x-105)=0

We get rid of parentheses

10x^2-30x+35x-105=0

We add all the numbers together, and all the variables

10x^2+5x-105=0

a = 10; b = 5; c = -105;
Δ = b2-4ac
Δ = 52-4·10·(-105)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-65}{2*10}=\frac{-70}{20}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+65}{2*10}=\frac{60}{20}
=3
$