69x2-x=45

Solution for 69x2-x=45 equation:

69x^2-x=45

We move all terms to the left:

69x^2-x-(45)=0

We add all the numbers together, and all the variables

69x^2-1x-45=0

a = 69; b = -1; c = -45;
Δ = b2-4ac
Δ = -12-4·69·(-45)
Δ = 12421
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{-(-1)-\sqrt{12421}}{2*69}=\frac{1-\sqrt{12421}}{138}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{12421}}{2*69}=\frac{1+\sqrt{12421}}{138}
$