1.5x(180-x)=70+x

Solution for 1.5x(180-x)=70+x equation:

1.5x(180-x)=70+x

We move all terms to the left:

1.5x(180-x)-(70+x)=0

We add all the numbers together, and all the variables

1.5x(-1x+180)-(x+70)=0

We multiply parentheses

-1x^2+180x-(x+70)=0

We get rid of parentheses

-1x^2+180x-x-70=0

We add all the numbers together, and all the variables

-1x^2+179x-70=0

a = -1; b = 179; c = -70;
Δ = b2-4ac
Δ = 1792-4·(-1)·(-70)
Δ = 31761
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:

$\sqrt{\Delta}=\sqrt{31761}=\sqrt{9*3529}=\sqrt{9}*\sqrt{3529}=3\sqrt{3529}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(179)-3\sqrt{3529}}{2*-1}=\frac{-179-3\sqrt{3529}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(179)+3\sqrt{3529}}{2*-1}=\frac{-179+3\sqrt{3529}}{-2}
$