(3/4)(4x+80)=90

Solution for (3/4)(4x+80)=90 equation:

(3/4)(4x+80)=90

We move all terms to the left:

(3/4)(4x+80)-(90)=0


Domain of the equation: 4)(4x+80)!=0

x∈R


We add all the numbers together, and all the variables

(+3/4)(4x+80)-90=0

We multiply parentheses ..

(+12x^2+3/4*80)-90=0

We multiply all the terms by the denominator


(+12x^2+3-90*4*80)=0

We get rid of parentheses

12x^2+3-90*4*80=0

We add all the numbers together, and all the variables

12x^2-28797=0

a = 12; b = 0; c = -28797;
Δ = b2-4ac
Δ = 02-4·12·(-28797)
Δ = 1382256
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:

$\sqrt{\Delta}=\sqrt{1382256}=\sqrt{144*9599}=\sqrt{144}*\sqrt{9599}=12\sqrt{9599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{9599}}{2*12}=\frac{0-12\sqrt{9599}}{24}
=-\frac{12\sqrt{9599}}{24}
=-\frac{\sqrt{9599}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{9599}}{2*12}=\frac{0+12\sqrt{9599}}{24}
=\frac{12\sqrt{9599}}{24}
=\frac{\sqrt{9599}}{2}
$