(7-0.75x)=-3/4x-7

Solution for (7-0.75x)=-3/4x-7 equation:

(7-0.75x)=-3/4x-7

We move all terms to the left:

(7-0.75x)-(-3/4x-7)=0


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

x∈R


We add all the numbers together, and all the variables

(-0.75x+7)-(-3/4x-7)=0

We get rid of parentheses

-0.75x+3/4x+7+7=0

We multiply all the terms by the denominator


-(0.75x)*4x+7*4x+7*4x+3=0

We add all the numbers together, and all the variables

-(+0.75x)*4x+7*4x+7*4x+3=0

We multiply parentheses

-0x^2+7*4x+7*4x+3=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-1x^2+56x+3=0

a = -1; b = 56; c = +3;
Δ = b2-4ac
Δ = 562-4·(-1)·3
Δ = 3148
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:

$\sqrt{\Delta}=\sqrt{3148}=\sqrt{4*787}=\sqrt{4}*\sqrt{787}=2\sqrt{787}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{787}}{2*-1}=\frac{-56-2\sqrt{787}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{787}}{2*-1}=\frac{-56+2\sqrt{787}}{-2}
$