x^2+2x=(42)/(8)

Solution for x^2+2x=(42)/(8) equation:

x^2+2x=(42)/(8)

We move all terms to the left:

x^2+2x-((42)/(8))=0

We add all the numbers together, and all the variables

x^2+2x-(+42/8)=0

We get rid of parentheses

x^2+2x-42/8=0

We multiply all the terms by the denominator


x^2*8+2x*8-42=0

Wy multiply elements

8x^2+16x-42=0

a = 8; b = 16; c = -42;
Δ = b2-4ac
Δ = 162-4·8·(-42)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-40}{2*8}=\frac{-56}{16}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+40}{2*8}=\frac{24}{16}
=1+1/2
$