90=0.5(5x+35)(x+2)

Solution for 90=0.5(5x+35)(x+2) equation:

90=0.5(5x+35)(x+2)

We move all terms to the left:

90-(0.5(5x+35)(x+2))=0

We multiply parentheses ..

-(0.5(+5x^2+10x+35x+70))+90=0


We calculate terms in parentheses: -(0.5(+5x^2+10x+35x+70)), so:

0.5(+5x^2+10x+35x+70)

We multiply parentheses

2.5x^2+5x+17.5x+35

We add all the numbers together, and all the variables

2.5x^2+22.5x+35

Back to the equation:

-(2.5x^2+22.5x+35)


We get rid of parentheses

-2.5x^2-22.5x-35+90=0

We add all the numbers together, and all the variables

-2.5x^2-22.5x+55=0

a = -2.5; b = -22.5; c = +55;
Δ = b2-4ac
Δ = -22.52-4·(-2.5)·55
Δ = 1056.25
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{-(-22.5)-\sqrt{1056.25}}{2*-2.5}=\frac{22.5-\sqrt{1056.25}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22.5)+\sqrt{1056.25}}{2*-2.5}=\frac{22.5+\sqrt{1056.25}}{-5}
$