(3x-10)(10x-27)=28

Solution for (3x-10)(10x-27)=28 equation:

(3x-10)(10x-27)=28

We move all terms to the left:

(3x-10)(10x-27)-(28)=0

We multiply parentheses ..

(+30x^2-81x-100x+270)-28=0

We get rid of parentheses

30x^2-81x-100x+270-28=0

We add all the numbers together, and all the variables

30x^2-181x+242=0

a = 30; b = -181; c = +242;
Δ = b2-4ac
Δ = -1812-4·30·242
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-181)-61}{2*30}=\frac{120}{60}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-181)+61}{2*30}=\frac{242}{60}
=4+1/30
$