(6x-5)(8x+23)=130

Solution for (6x-5)(8x+23)=130 equation:

(6x-5)(8x+23)=130

We move all terms to the left:

(6x-5)(8x+23)-(130)=0

We multiply parentheses ..

(+48x^2+138x-40x-115)-130=0

We get rid of parentheses

48x^2+138x-40x-115-130=0

We add all the numbers together, and all the variables

48x^2+98x-245=0

a = 48; b = 98; c = -245;
Δ = b2-4ac
Δ = 982-4·48·(-245)
Δ = 56644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{56644}=238$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-238}{2*48}=\frac{-336}{96}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+238}{2*48}=\frac{140}{96}
=1+11/24
$