x(5x+11)=2x^2-5x+64

Solution for x(5x+11)=2x^2-5x+64 equation:

x(5x+11)=2x^2-5x+64

We move all terms to the left:

x(5x+11)-(2x^2-5x+64)=0

We multiply parentheses

5x^2+11x-(2x^2-5x+64)=0

We get rid of parentheses

5x^2-2x^2+11x+5x-64=0

We add all the numbers together, and all the variables

3x^2+16x-64=0

a = 3; b = 16; c = -64;
Δ = b2-4ac
Δ = 162-4·3·(-64)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-32}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+32}{2*3}=\frac{16}{6}
=2+2/3
$