0=(2x+7)(3x-5)

Solution for 0=(2x+7)(3x-5) equation:

0=(2x+7)(3x-5)

We move all terms to the left:

0-((2x+7)(3x-5))=0

We add all the numbers together, and all the variables

-((2x+7)(3x-5))=0

We multiply parentheses ..

-((+6x^2-10x+21x-35))=0


We calculate terms in parentheses: -((+6x^2-10x+21x-35)), so:

(+6x^2-10x+21x-35)

We get rid of parentheses

6x^2-10x+21x-35

We add all the numbers together, and all the variables

6x^2+11x-35

Back to the equation:

-(6x^2+11x-35)


We get rid of parentheses

-6x^2-11x+35=0

a = -6; b = -11; c = +35;
Δ = b2-4ac
Δ = -112-4·(-6)·35
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-31}{2*-6}=\frac{-20}{-12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*-6}=\frac{42}{-12}
=-3+1/2
$