X-7=3/4x-5

Solution for X-7=3/4x-5 equation:

X-7=3/4X-5

We move all terms to the left:

X-7-(3/4X-5)=0


Domain of the equation: 4X-5)!=0

X∈R


We get rid of parentheses

X-3/4X+5-7=0

We multiply all the terms by the denominator


X*4X+5*4X-7*4X-3=0

Wy multiply elements

4X^2+20X-28X-3=0

We add all the numbers together, and all the variables

4X^2-8X-3=0

a = 4; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·4·(-3)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*4}=\frac{8-4\sqrt{7}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*4}=\frac{8+4\sqrt{7}}{8}
$