(6x+1)(8x-23)=90

Solution for (6x+1)(8x-23)=90 equation:

(6x+1)(8x-23)=90

We move all terms to the left:

(6x+1)(8x-23)-(90)=0

We multiply parentheses ..

(+48x^2-138x+8x-23)-90=0

We get rid of parentheses

48x^2-138x+8x-23-90=0

We add all the numbers together, and all the variables

48x^2-130x-113=0

a = 48; b = -130; c = -113;
Δ = b2-4ac
Δ = -1302-4·48·(-113)
Δ = 38596
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:

$\sqrt{\Delta}=\sqrt{38596}=\sqrt{4*9649}=\sqrt{4}*\sqrt{9649}=2\sqrt{9649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{9649}}{2*48}=\frac{130-2\sqrt{9649}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{9649}}{2*48}=\frac{130+2\sqrt{9649}}{96}
$