(2x+15)(2x+30)=1000

Solution for (2x+15)(2x+30)=1000 equation:

(2x+15)(2x+30)=1000

We move all terms to the left:

(2x+15)(2x+30)-(1000)=0

We multiply parentheses ..

(+4x^2+60x+30x+450)-1000=0

We get rid of parentheses

4x^2+60x+30x+450-1000=0

We add all the numbers together, and all the variables

4x^2+90x-550=0

a = 4; b = 90; c = -550;
Δ = b2-4ac
Δ = 902-4·4·(-550)
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-130}{2*4}=\frac{-220}{8}
=-27+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+130}{2*4}=\frac{40}{8}
=5
$