(3x+7)(4x-11)=0

Solution for (3x+7)(4x-11)=0 equation:

(3x+7)(4x-11)=0

We multiply parentheses ..

(+12x^2-33x+28x-77)=0

We get rid of parentheses

12x^2-33x+28x-77=0

We add all the numbers together, and all the variables

12x^2-5x-77=0

a = 12; b = -5; c = -77;
Δ = b2-4ac
Δ = -52-4·12·(-77)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-61}{2*12}=\frac{-56}{24}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+61}{2*12}=\frac{66}{24}
=2+3/4
$