(3x-7)(8x-24)=90

Solution for (3x-7)(8x-24)=90 equation:

(3x-7)(8x-24)=90

We move all terms to the left:

(3x-7)(8x-24)-(90)=0

We multiply parentheses ..

(+24x^2-72x-56x+168)-90=0

We get rid of parentheses

24x^2-72x-56x+168-90=0

We add all the numbers together, and all the variables

24x^2-128x+78=0

a = 24; b = -128; c = +78;
Δ = b2-4ac
Δ = -1282-4·24·78
Δ = 8896
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:

$\sqrt{\Delta}=\sqrt{8896}=\sqrt{64*139}=\sqrt{64}*\sqrt{139}=8\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-8\sqrt{139}}{2*24}=\frac{128-8\sqrt{139}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+8\sqrt{139}}{2*24}=\frac{128+8\sqrt{139}}{48}
$