(4x-10)(6x-18)=90

Solution for (4x-10)(6x-18)=90 equation:

(4x-10)(6x-18)=90

We move all terms to the left:

(4x-10)(6x-18)-(90)=0

We multiply parentheses ..

(+24x^2-72x-60x+180)-90=0

We get rid of parentheses

24x^2-72x-60x+180-90=0

We add all the numbers together, and all the variables

24x^2-132x+90=0

a = 24; b = -132; c = +90;
Δ = b2-4ac
Δ = -1322-4·24·90
Δ = 8784
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:

$\sqrt{\Delta}=\sqrt{8784}=\sqrt{144*61}=\sqrt{144}*\sqrt{61}=12\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-12\sqrt{61}}{2*24}=\frac{132-12\sqrt{61}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+12\sqrt{61}}{2*24}=\frac{132+12\sqrt{61}}{48}
$