6(x-2)2x-3(x-5)=7

Solution for 6(x-2)2x-3(x-5)=7 equation:

6(x-2)2x-3(x-5)=7

We move all terms to the left:

6(x-2)2x-3(x-5)-(7)=0

We multiply parentheses

12x^2-24x-3x+15-7=0

We add all the numbers together, and all the variables

12x^2-27x+8=0

a = 12; b = -27; c = +8;
Δ = b2-4ac
Δ = -272-4·12·8
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{345}}{2*12}=\frac{27-\sqrt{345}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{345}}{2*12}=\frac{27+\sqrt{345}}{24}
$