(-7x+5/4x-3)=5

Solution for (-7x+5/4x-3)=5 equation:

(-7x+5/4x-3)=5

We move all terms to the left:

(-7x+5/4x-3)-(5)=0


Domain of the equation: 4x-3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-28x^2-12x-20x+5=0

We add all the numbers together, and all the variables

-28x^2-32x+5=0

a = -28; b = -32; c = +5;
Δ = b2-4ac
Δ = -322-4·(-28)·5
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-12\sqrt{11}}{2*-28}=\frac{32-12\sqrt{11}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+12\sqrt{11}}{2*-28}=\frac{32+12\sqrt{11}}{-56}
$