X2+6y=3/4

Solution for X2+6y=3/4 equation:

X2+6X=3/4

We move all terms to the left:

X2+6X-(3/4)=0

We add all the numbers together, and all the variables

X2+6X-(+3/4)=0

We add all the numbers together, and all the variables

X^2+6X-(+3/4)=0

We get rid of parentheses

X^2+6X-3/4=0

We multiply all the terms by the denominator


X^2*4+6X*4-3=0

Wy multiply elements

4X^2+24X-3=0

a = 4; b = 24; c = -3;
Δ = b2-4ac
Δ = 242-4·4·(-3)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{39}}{2*4}=\frac{-24-4\sqrt{39}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{39}}{2*4}=\frac{-24+4\sqrt{39}}{8}
$