x*(4x-7)=47+4x-7

Solution for x*(4x-7)=47+4x-7 equation:

x(4x-7)=47+4x-7

We move all terms to the left:

x(4x-7)-(47+4x-7)=0

We add all the numbers together, and all the variables

x(4x-7)-(4x+40)=0

We multiply parentheses

4x^2-7x-(4x+40)=0

We get rid of parentheses

4x^2-7x-4x-40=0

We add all the numbers together, and all the variables

4x^2-11x-40=0

a = 4; b = -11; c = -40;
Δ = b2-4ac
Δ = -112-4·4·(-40)
Δ = 761
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{-(-11)-\sqrt{761}}{2*4}=\frac{11-\sqrt{761}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{761}}{2*4}=\frac{11+\sqrt{761}}{8}
$