3/4x+8=x-7

Solution for 3/4x+8=x-7 equation:

3/4x+8=x-7

We move all terms to the left:

3/4x+8-(x-7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-x+7+8=0

We multiply all the terms by the denominator


-x*4x+7*4x+8*4x+3=0

Wy multiply elements

-4x^2+28x+32x+3=0

We add all the numbers together, and all the variables

-4x^2+60x+3=0

a = -4; b = 60; c = +3;
Δ = b2-4ac
Δ = 602-4·(-4)·3
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-8\sqrt{57}}{2*-4}=\frac{-60-8\sqrt{57}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+8\sqrt{57}}{2*-4}=\frac{-60+8\sqrt{57}}{-8}
$