(8x-1)(6x+15)=43

Solution for (8x-1)(6x+15)=43 equation:

(8x-1)(6x+15)=43

We move all terms to the left:

(8x-1)(6x+15)-(43)=0

We multiply parentheses ..

(+48x^2+120x-6x-15)-43=0

We get rid of parentheses

48x^2+120x-6x-15-43=0

We add all the numbers together, and all the variables

48x^2+114x-58=0

a = 48; b = 114; c = -58;
Δ = b2-4ac
Δ = 1142-4·48·(-58)
Δ = 24132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24132}=\sqrt{4*6033}=\sqrt{4}*\sqrt{6033}=2\sqrt{6033}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-2\sqrt{6033}}{2*48}=\frac{-114-2\sqrt{6033}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+2\sqrt{6033}}{2*48}=\frac{-114+2\sqrt{6033}}{96}
$