x^2-7x+49/4=-6+49/4

Solution for x^2-7x+49/4=-6+49/4 equation:

x^2-7x+49/4=-6+49/4

We move all terms to the left:

x^2-7x+49/4-(-6+49/4)=0

We add all the numbers together, and all the variables

x^2-7x+49/4-(49/4-6)=0

We get rid of parentheses

x^2-7x+6+49/4-49/4=0

We multiply all the terms by the denominator


x^2*4-7x*4+49-49+6*4=0

We add all the numbers together, and all the variables

x^2*4-7x*4+24=0

Wy multiply elements

4x^2-28x+24=0

a = 4; b = -28; c = +24;
Δ = b2-4ac
Δ = -282-4·4·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-20}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+20}{2*4}=\frac{48}{8}
=6
$