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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+7)!=0

x∈R


We multiply parentheses

4x-(3/2x+7)-32=0

We get rid of parentheses

4x-3/2x-7-32=0

We multiply all the terms by the denominator


4x*2x-7*2x-32*2x-3=0

Wy multiply elements

8x^2-14x-64x-3=0

We add all the numbers together, and all the variables

8x^2-78x-3=0

a = 8; b = -78; c = -3;
Δ = b2-4ac
Δ = -782-4·8·(-3)
Δ = 6180
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:

$\sqrt{\Delta}=\sqrt{6180}=\sqrt{4*1545}=\sqrt{4}*\sqrt{1545}=2\sqrt{1545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1545}}{2*8}=\frac{78-2\sqrt{1545}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1545}}{2*8}=\frac{78+2\sqrt{1545}}{16}
$