4x^2+10=-2x+40

Solution for 4x^2+10=-2x+40 equation:

4x^2+10=-2x+40

We move all terms to the left:

4x^2+10-(-2x+40)=0

We get rid of parentheses

4x^2+2x-40+10=0

We add all the numbers together, and all the variables

4x^2+2x-30=0

a = 4; b = 2; c = -30;
Δ = b2-4ac
Δ = 22-4·4·(-30)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*4}=\frac{20}{8}
=2+1/2
$