(5x+14)(3x=18)

Solution for (5x+14)(3x=18) equation:

(5x+14)(3x=18)

We move all terms to the left:

(5x+14)(3x-(18))=0

We multiply parentheses ..

(+15x^2-90x+42x-252)=0

We get rid of parentheses

15x^2-90x+42x-252=0

We add all the numbers together, and all the variables

15x^2-48x-252=0

a = 15; b = -48; c = -252;
Δ = b2-4ac
Δ = -482-4·15·(-252)
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-132}{2*15}=\frac{-84}{30}
=-2+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+132}{2*15}=\frac{180}{30}
=6
$