x^2-7x+(7/4)=-4

Solution for x^2-7x+(7/4)=-4 equation:

x^2-7x+(7/4)=-4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x^2*4-7x*4+23=0

Wy multiply elements

4x^2-28x+23=0

a = 4; b = -28; c = +23;
Δ = b2-4ac
Δ = -282-4·4·23
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{26}}{2*4}=\frac{28-4\sqrt{26}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{26}}{2*4}=\frac{28+4\sqrt{26}}{8}
$