X^2+7x=207/4

Solution for X^2+7x=207/4 equation:

X^2+7X=207/4

We move all terms to the left:

X^2+7X-(207/4)=0

We add all the numbers together, and all the variables

X^2+7X-(+207/4)=0

We get rid of parentheses

X^2+7X-207/4=0

We multiply all the terms by the denominator


X^2*4+7X*4-207=0

Wy multiply elements

4X^2+28X-207=0

a = 4; b = 28; c = -207;
Δ = b2-4ac
Δ = 282-4·4·(-207)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-64}{2*4}=\frac{-92}{8}
=-11+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+64}{2*4}=\frac{36}{8}
=4+1/2
$