X-11=3/4x-5

Solution for X-11=3/4x-5 equation:

X-11=3/4X-5

We move all terms to the left:

X-11-(3/4X-5)=0


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

X∈R


We get rid of parentheses

X-3/4X+5-11=0

We multiply all the terms by the denominator


X*4X+5*4X-11*4X-3=0

Wy multiply elements

4X^2+20X-44X-3=0

We add all the numbers together, and all the variables

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}
$