3/4x+8=2x-7

Solution for 3/4x+8=2x-7 equation:

3/4x+8=2x-7

We move all terms to the left:

3/4x+8-(2x-7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-2x+7+8=0

We multiply all the terms by the denominator


-2x*4x+7*4x+8*4x+3=0

Wy multiply elements

-8x^2+28x+32x+3=0

We add all the numbers together, and all the variables

-8x^2+60x+3=0

a = -8; b = 60; c = +3;
Δ = b2-4ac
Δ = 602-4·(-8)·3
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{231}}{2*-8}=\frac{-60-4\sqrt{231}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{231}}{2*-8}=\frac{-60+4\sqrt{231}}{-16}
$