6x^2+2x-11-52+45x=0

Solution for 6x^2+2x-11-52+45x=0 equation:

6x^2+2x-11-52+45x=0

We add all the numbers together, and all the variables

6x^2+47x-63=0

a = 6; b = 47; c = -63;
Δ = b2-4ac
Δ = 472-4·6·(-63)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-61}{2*6}=\frac{-108}{12}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+61}{2*6}=\frac{14}{12}
=1+1/6
$