4(x+2)(3x-7)=22-65

Solution for 4(x+2)(3x-7)=22-65 equation:

4(x+2)(3x-7)=22-65

We move all terms to the left:

4(x+2)(3x-7)-(22-65)=0

We add all the numbers together, and all the variables

4(x+2)(3x-7)-(-43)=0

We add all the numbers together, and all the variables

4(x+2)(3x-7)+43=0

We multiply parentheses ..

4(+3x^2-7x+6x-14)+43=0

We multiply parentheses

12x^2-28x+24x-56+43=0

We add all the numbers together, and all the variables

12x^2-4x-13=0

a = 12; b = -4; c = -13;
Δ = b2-4ac
Δ = -42-4·12·(-13)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{10}}{2*12}=\frac{4-8\sqrt{10}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{10}}{2*12}=\frac{4+8\sqrt{10}}{24}
$