(2x+7)(3x-5)=54

Solution for (2x+7)(3x-5)=54 equation:

(2x+7)(3x-5)=54

We move all terms to the left:

(2x+7)(3x-5)-(54)=0

We multiply parentheses ..

(+6x^2-10x+21x-35)-54=0

We get rid of parentheses

6x^2-10x+21x-35-54=0

We add all the numbers together, and all the variables

6x^2+11x-89=0

a = 6; b = 11; c = -89;
Δ = b2-4ac
Δ = 112-4·6·(-89)
Δ = 2257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{2257}}{2*6}=\frac{-11-\sqrt{2257}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{2257}}{2*6}=\frac{-11+\sqrt{2257}}{12}
$