(3x+11)(7x+2)=0

Solution for (3x+11)(7x+2)=0 equation:

(3x+11)(7x+2)=0

We multiply parentheses ..

(+21x^2+6x+77x+22)=0

We get rid of parentheses

21x^2+6x+77x+22=0

We add all the numbers together, and all the variables

21x^2+83x+22=0

a = 21; b = 83; c = +22;
Δ = b2-4ac
Δ = 832-4·21·22
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(83)-71}{2*21}=\frac{-154}{42}
=-3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(83)+71}{2*21}=\frac{-12}{42}
=-2/7
$