28x-60,5(11x-128)=6x(5-0,25x)+3(2x+58)

Solution for 28x-60,5(11x-128)=6x(5-0,25x)+3(2x+58) equation:

28x-60.5(11x-128)=6x(5-0.25x)+3(2x+58)

We move all terms to the left:

28x-60.5(11x-128)-(6x(5-0.25x)+3(2x+58))=0

We add all the numbers together, and all the variables

28x-60.5(11x-128)-(6x(-0.25x+5)+3(2x+58))=0

We multiply parentheses

28x-665.5x-(6x(-0.25x+5)+3(2x+58))+7744=0


We calculate terms in parentheses: -(6x(-0.25x+5)+3(2x+58)), so:

6x(-0.25x+5)+3(2x+58)

We multiply parentheses

0x^2+30x+6x+174

We add all the numbers together, and all the variables

x^2+36x+174

Back to the equation:

-(x^2+36x+174)


We add all the numbers together, and all the variables

-637.5x-(x^2+36x+174)+7744=0

We get rid of parentheses

-x^2-637.5x-36x-174+7744=0

We add all the numbers together, and all the variables

-1x^2-673.5x+7570=0

a = -1; b = -673.5; c = +7570;
Δ = b2-4ac
Δ = -673.52-4·(-1)·7570
Δ = 483882.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-673.5)-\sqrt{483882.25}}{2*-1}=\frac{673.5-\sqrt{483882.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-673.5)+\sqrt{483882.25}}{2*-1}=\frac{673.5+\sqrt{483882.25}}{-2}
$