(4x-19)(7x+18)=0

Solution for (4x-19)(7x+18)=0 equation:

(4x-19)(7x+18)=0

We multiply parentheses ..

(+28x^2+72x-133x-342)=0

We get rid of parentheses

28x^2+72x-133x-342=0

We add all the numbers together, and all the variables

28x^2-61x-342=0

a = 28; b = -61; c = -342;
Δ = b2-4ac
Δ = -612-4·28·(-342)
Δ = 42025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{42025}=205$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-205}{2*28}=\frac{-144}{56}
=-2+4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+205}{2*28}=\frac{266}{56}
=4+3/4
$