(x+6)(3x-1)+(8x-9)(4x-3=)

Solution for (x+6)(3x-1)+(8x-9)(4x-3=) equation:

(x+6)(3x-1)+(8x-9)(4x-3=)

We move all terms to the left:

(x+6)(3x-1)+(8x-9)(4x-3-())=0

We multiply parentheses ..

(+3x^2-1x+18x-6)+(8x-9)(4x-3-())=0


We calculate terms in parentheses: +(8x-9)(4x-3-()), so:

8x-9)(4x-3-()

We add all the numbers together, and all the variables

8x-9)(4x

Back to the equation:

+(8x-9)(4x)


We multiply parentheses

(+3x^2-1x+18x-6)+32x^2-36x=0

We get rid of parentheses

3x^2+32x^2-1x+18x-36x-6=0

We add all the numbers together, and all the variables

35x^2-19x-6=0

a = 35; b = -19; c = -6;
Δ = b2-4ac
Δ = -192-4·35·(-6)
Δ = 1201
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{-(-19)-\sqrt{1201}}{2*35}=\frac{19-\sqrt{1201}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1201}}{2*35}=\frac{19+\sqrt{1201}}{70}
$