x(7x+3)=2x^2-36x+54

Solution for x(7x+3)=2x^2-36x+54 equation:

x(7x+3)=2x^2-36x+54

We move all terms to the left:

x(7x+3)-(2x^2-36x+54)=0

We multiply parentheses

7x^2+3x-(2x^2-36x+54)=0

We get rid of parentheses

7x^2-2x^2+3x+36x-54=0

We add all the numbers together, and all the variables

5x^2+39x-54=0

a = 5; b = 39; c = -54;
Δ = b2-4ac
Δ = 392-4·5·(-54)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-51}{2*5}=\frac{-90}{10}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+51}{2*5}=\frac{12}{10}
=1+1/5
$