-10x^2-12x+45=-9x^2+1x-5x

Solution for -10x^2-12x+45=-9x^2+1x-5x equation:

-10x^2-12x+45=-9x^2+1x-5x

We move all terms to the left:

-10x^2-12x+45-(-9x^2+1x-5x)=0

We get rid of parentheses

-10x^2+9x^2-1x+5x-12x+45=0

We add all the numbers together, and all the variables

-1x^2-8x+45=0

a = -1; b = -8; c = +45;
Δ = b2-4ac
Δ = -82-4·(-1)·45
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{61}}{2*-1}=\frac{8-2\sqrt{61}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{61}}{2*-1}=\frac{8+2\sqrt{61}}{-2}
$