x(7x+16)=2x^2-3x+30

Solution for x(7x+16)=2x^2-3x+30 equation:

x(7x+16)=2x^2-3x+30

We move all terms to the left:

x(7x+16)-(2x^2-3x+30)=0

We multiply parentheses

7x^2+16x-(2x^2-3x+30)=0

We get rid of parentheses

7x^2-2x^2+16x+3x-30=0

We add all the numbers together, and all the variables

5x^2+19x-30=0

a = 5; b = 19; c = -30;
Δ = b2-4ac
Δ = 192-4·5·(-30)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-31}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+31}{2*5}=\frac{12}{10}
=1+1/5
$