-6x+20=-3/4x-7

Solution for -6x+20=-3/4x-7 equation:

-6x+20=-3/4x-7

We move all terms to the left:

-6x+20-(-3/4x-7)=0


Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

-6x+3/4x+7+20=0

We multiply all the terms by the denominator


-6x*4x+7*4x+20*4x+3=0

Wy multiply elements

-24x^2+28x+80x+3=0

We add all the numbers together, and all the variables

-24x^2+108x+3=0

a = -24; b = 108; c = +3;
Δ = b2-4ac
Δ = 1082-4·(-24)·3
Δ = 11952
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:

$\sqrt{\Delta}=\sqrt{11952}=\sqrt{144*83}=\sqrt{144}*\sqrt{83}=12\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-12\sqrt{83}}{2*-24}=\frac{-108-12\sqrt{83}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+12\sqrt{83}}{2*-24}=\frac{-108+12\sqrt{83}}{-48}
$