3(2.7x+4)-1.6x=5(1.3x+7)x-10.11

Solution for 3(2.7x+4)-1.6x=5(1.3x+7)x-10.11 equation:

3(2.7x+4)-1.6x=5(1.3x+7)x-10.11

We move all terms to the left:

3(2.7x+4)-1.6x-(5(1.3x+7)x-10.11)=0

We add all the numbers together, and all the variables

-1.6x+3(2.7x+4)-(5(1.3x+7)x-10.11)=0

We multiply parentheses

-1.6x+6x-(5(1.3x+7)x-10.11)+12=0


We calculate terms in parentheses: -(5(1.3x+7)x-10.11), so:

5(1.3x+7)x-10.11

We multiply parentheses

5x^2+35x-10.11

Back to the equation:

-(5x^2+35x-10.11)


We add all the numbers together, and all the variables

4.4x-(5x^2+35x-10.11)+12=0

We get rid of parentheses

-5x^2+4.4x-35x+10.11+12=0

We add all the numbers together, and all the variables

-5x^2-30.6x+22.11=0

a = -5; b = -30.6; c = +22.11;
Δ = b2-4ac
Δ = -30.62-4·(-5)·22.11
Δ = 1378.56
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{-(-30.6)-\sqrt{1378.56}}{2*-5}=\frac{30.6-\sqrt{1378.56}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30.6)+\sqrt{1378.56}}{2*-5}=\frac{30.6+\sqrt{1378.56}}{-10}
$