6x-10=-2x^2

Solution for 6x-10=-2x^2 equation:

6x-10=-2x^2

We move all terms to the left:

6x-10-(-2x^2)=0

We get rid of parentheses

2x^2+6x-10=0

a = 2; b = 6; c = -10;
Δ = b2-4ac
Δ = 62-4·2·(-10)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{29}}{2*2}=\frac{-6-2\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{29}}{2*2}=\frac{-6+2\sqrt{29}}{4}
$