9x(5x-2)=-12+45x^

Solution for 9x(5x-2)=-12+45x^ equation:

9x(5x-2)=-12+45x^

We move all terms to the left:

9x(5x-2)-(-12+45x^)=0

We multiply parentheses

45x^2-18x-(-12+45x^)=0

We get rid of parentheses

45x^2-18x-45x^+12=0

We add all the numbers together, and all the variables

45x^2-63x+12=0

a = 45; b = -63; c = +12;
Δ = b2-4ac
Δ = -632-4·45·12
Δ = 1809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1809}=\sqrt{9*201}=\sqrt{9}*\sqrt{201}=3\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{201}}{2*45}=\frac{63-3\sqrt{201}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{201}}{2*45}=\frac{63+3\sqrt{201}}{90}
$