(10x-23)(3x=19)

Solution for (10x-23)(3x=19) equation:

(10x-23)(3x=19)

We move all terms to the left:

(10x-23)(3x-(19))=0

We multiply parentheses ..

(+30x^2-190x-69x+437)=0

We get rid of parentheses

30x^2-190x-69x+437=0

We add all the numbers together, and all the variables

30x^2-259x+437=0

a = 30; b = -259; c = +437;
Δ = b2-4ac
Δ = -2592-4·30·437
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-259)-121}{2*30}=\frac{138}{60}
=2+3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-259)+121}{2*30}=\frac{380}{60}
=6+1/3
$