84x(x+2)=90-13x

Solution for 84x(x+2)=90-13x equation:

84x(x+2)=90-13x

We move all terms to the left:

84x(x+2)-(90-13x)=0

We add all the numbers together, and all the variables

84x(x+2)-(-13x+90)=0

We multiply parentheses

84x^2+168x-(-13x+90)=0

We get rid of parentheses

84x^2+168x+13x-90=0

We add all the numbers together, and all the variables

84x^2+181x-90=0

a = 84; b = 181; c = -90;
Δ = b2-4ac
Δ = 1812-4·84·(-90)
Δ = 63001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63001}=251$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(181)-251}{2*84}=\frac{-432}{168}
=-2+4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(181)+251}{2*84}=\frac{70}{168}
=5/12
$