3(7x-1)4-(2x-1-x2)=x+32

Solution for 3(7x-1)4-(2x-1-x2)=x+32 equation:

3(7x-1)4-(2x-1-x2)=x+32

We move all terms to the left:

3(7x-1)4-(2x-1-x2)-(x+32)=0

We add all the numbers together, and all the variables

-(+2x-1x^2-1)+3(7x-1)4-(x+32)=0

We multiply parentheses

-(+2x-1x^2-1)+84x-(x+32)-12=0

We get rid of parentheses

1x^2-2x+84x-x+1-32-12=0

We add all the numbers together, and all the variables

x^2+81x-43=0

a = 1; b = 81; c = -43;
Δ = b2-4ac
Δ = 812-4·1·(-43)
Δ = 6733
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{-(81)-\sqrt{6733}}{2*1}=\frac{-81-\sqrt{6733}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+\sqrt{6733}}{2*1}=\frac{-81+\sqrt{6733}}{2}
$