7=3x(x-1)+4(x-1)

Solution for 7=3x(x-1)+4(x-1) equation:

7=3x(x-1)+4(x-1)

We move all terms to the left:

7-(3x(x-1)+4(x-1))=0


We calculate terms in parentheses: -(3x(x-1)+4(x-1)), so:

3x(x-1)+4(x-1)

We multiply parentheses

3x^2-3x+4x-4

We add all the numbers together, and all the variables

3x^2+x-4

Back to the equation:

-(3x^2+x-4)


We get rid of parentheses

-3x^2-x+4+7=0

We add all the numbers together, and all the variables

-3x^2-1x+11=0

a = -3; b = -1; c = +11;
Δ = b2-4ac
Δ = -12-4·(-3)·11
Δ = 133
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{-(-1)-\sqrt{133}}{2*-3}=\frac{1-\sqrt{133}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{133}}{2*-3}=\frac{1+\sqrt{133}}{-6}
$