(5x-7)(3x+11)=0

Solution for (5x-7)(3x+11)=0 equation:

(5x-7)(3x+11)=0

We multiply parentheses ..

(+15x^2+55x-21x-77)=0

We get rid of parentheses

15x^2+55x-21x-77=0

We add all the numbers together, and all the variables

15x^2+34x-77=0

a = 15; b = 34; c = -77;
Δ = b2-4ac
Δ = 342-4·15·(-77)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-76}{2*15}=\frac{-110}{30}
=-3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+76}{2*15}=\frac{42}{30}
=1+2/5
$