X^2-4x^2+6x-10x=-5

Solution for X^2-4x^2+6x-10x=-5 equation:

X^2-4X^2+6X-10X=-5

We move all terms to the left:

X^2-4X^2+6X-10X-(-5)=0

We add all the numbers together, and all the variables

-3X^2-4X+5=0

a = -3; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-3)·5
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{19}}{2*-3}=\frac{4-2\sqrt{19}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{19}}{2*-3}=\frac{4+2\sqrt{19}}{-6}
$