8x^2+6x+20=-4x+83

Solution for 8x^2+6x+20=-4x+83 equation:

8x^2+6x+20=-4x+83

We move all terms to the left:

8x^2+6x+20-(-4x+83)=0

We get rid of parentheses

8x^2+6x+4x-83+20=0

We add all the numbers together, and all the variables

8x^2+10x-63=0

a = 8; b = 10; c = -63;
Δ = b2-4ac
Δ = 102-4·8·(-63)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-46}{2*8}=\frac{-56}{16}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+46}{2*8}=\frac{36}{16}
=2+1/4
$