-8x+10=3x2=-2x

Solution for -8x+10=3x2=-2x equation:

-8x+10=3x^2=-2x

We move all terms to the left:

-8x+10-(3x^2)=0

determiningTheFunctionDomain
-3x^2-8x+10=0

a = -3; b = -8; c = +10;
Δ = b2-4ac
Δ = -82-4·(-3)·10
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{46}}{2*-3}=\frac{8-2\sqrt{46}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{46}}{2*-3}=\frac{8+2\sqrt{46}}{-6}
$