-29.145=-6(10+x)+15(10+x)-50x^2

Solution for -29.145=-6(10+x)+15(10+x)-50x^2 equation:

-29.145=-6(10+x)+15(10+x)-50x^2

We move all terms to the left:

-29.145-(-6(10+x)+15(10+x)-50x^2)=0

We add all the numbers together, and all the variables

-(-6(x+10)+15(x+10)-50x^2)-29.145=0


We calculate terms in parentheses: -(-6(x+10)+15(x+10)-50x^2), so:

-6(x+10)+15(x+10)-50x^2

determiningTheFunctionDomain
-50x^2-6(x+10)+15(x+10)

We multiply parentheses

-50x^2-6x+15x-60+150

We add all the numbers together, and all the variables

-50x^2+9x+90

Back to the equation:

-(-50x^2+9x+90)


We get rid of parentheses

50x^2-9x-90-29.145=0

We add all the numbers together, and all the variables

50x^2-9x-119.145=0

a = 50; b = -9; c = -119.145;
Δ = b2-4ac
Δ = -92-4·50·(-119.145)
Δ = 23910
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{-(-9)-\sqrt{23910}}{2*50}=\frac{9-\sqrt{23910}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{23910}}{2*50}=\frac{9+\sqrt{23910}}{100}
$