7.4(9.5x-80)=99-5/12x

Solution for 7.4(9.5x-80)=99-5/12x equation:

7.4(9.5x-80)=99-5/12x

We move all terms to the left:

7.4(9.5x-80)-(99-5/12x)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7.4(9.5x-80)-(-5/12x+99)=0

We multiply parentheses

66.6x-(-5/12x+99)-592=0

We get rid of parentheses

66.6x+5/12x-99-592=0

We multiply all the terms by the denominator


(66.6x)*12x-99*12x-592*12x+5=0

We add all the numbers together, and all the variables

(+66.6x)*12x-99*12x-592*12x+5=0

We multiply parentheses

792x^2-99*12x-592*12x+5=0

Wy multiply elements

792x^2-1188x-7104x+5=0

We add all the numbers together, and all the variables

792x^2-8292x+5=0

a = 792; b = -8292; c = +5;
Δ = b2-4ac
Δ = -82922-4·792·5
Δ = 68741424
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:

$\sqrt{\Delta}=\sqrt{68741424}=\sqrt{144*477371}=\sqrt{144}*\sqrt{477371}=12\sqrt{477371}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8292)-12\sqrt{477371}}{2*792}=\frac{8292-12\sqrt{477371}}{1584}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8292)+12\sqrt{477371}}{2*792}=\frac{8292+12\sqrt{477371}}{1584}
$