0.8(x+20)-4.5=0.7(5+x)0.9x

Solution for 0.8(x+20)-4.5=0.7(5+x)0.9x equation:

0.8(x+20)-4.5=0.7(5+x)0.9x

We move all terms to the left:

0.8(x+20)-4.5-(0.7(5+x)0.9x)=0

We add all the numbers together, and all the variables

0.8(x+20)-(0.7(x+5)0.9x)-4.5=0

We multiply parentheses

0.8x-(0.7(x+5)0.9x)+16-4.5=0


We calculate terms in parentheses: -(0.7(x+5)0.9x), so:

0.7(x+5)0.9x

We multiply parentheses

0x^2+0x

We add all the numbers together, and all the variables

x^2+x

Back to the equation:

-(x^2+x)


We add all the numbers together, and all the variables

0.8x-(x^2+x)+11.5=0

We get rid of parentheses

-x^2+0.8x-x+11.5=0

We add all the numbers together, and all the variables

-1x^2-0.2x+11.5=0

a = -1; b = -0.2; c = +11.5;
Δ = b2-4ac
Δ = -0.22-4·(-1)·11.5
Δ = 46.04
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{-(-0.2)-\sqrt{46.04}}{2*-1}=\frac{0.2-\sqrt{46.04}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{46.04}}{2*-1}=\frac{0.2+\sqrt{46.04}}{-2}
$