(23+7x)(9x+34)=0

Solution for (23+7x)(9x+34)=0 equation:

(23+7x)(9x+34)=0

We add all the numbers together, and all the variables

(7x+23)(9x+34)=0

We multiply parentheses ..

(+63x^2+238x+207x+782)=0

We get rid of parentheses

63x^2+238x+207x+782=0

We add all the numbers together, and all the variables

63x^2+445x+782=0

a = 63; b = 445; c = +782;
Δ = b2-4ac
Δ = 4452-4·63·782
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{-(445)-31}{2*63}=\frac{-476}{126}
=-3+7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(445)+31}{2*63}=\frac{-414}{126}
=-3+2/7
$