(3x-14)(2x+10)=140

Solution for (3x-14)(2x+10)=140 equation:

(3x-14)(2x+10)=140

We move all terms to the left:

(3x-14)(2x+10)-(140)=0

We multiply parentheses ..

(+6x^2+30x-28x-140)-140=0

We get rid of parentheses

6x^2+30x-28x-140-140=0

We add all the numbers together, and all the variables

6x^2+2x-280=0

a = 6; b = 2; c = -280;
Δ = b2-4ac
Δ = 22-4·6·(-280)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-82}{2*6}=\frac{-84}{12}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+82}{2*6}=\frac{80}{12}
=6+2/3
$