(25x^2-50x+75)-100x^2-50x-150)=0

Solution for (25x^2-50x+75)-100x^2-50x-150)=0 equation:

(25x^2-50x+75)-100x^2-50x-150)=0

We add all the numbers together, and all the variables

-100x^2-50x+(25x^2-50x+75)=0

We get rid of parentheses

-100x^2+25x^2-50x-50x+75=0

We add all the numbers together, and all the variables

-75x^2-100x+75=0

a = -75; b = -100; c = +75;
Δ = b2-4ac
Δ = -1002-4·(-75)·75
Δ = 32500
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:

$\sqrt{\Delta}=\sqrt{32500}=\sqrt{2500*13}=\sqrt{2500}*\sqrt{13}=50\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-50\sqrt{13}}{2*-75}=\frac{100-50\sqrt{13}}{-150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+50\sqrt{13}}{2*-75}=\frac{100+50\sqrt{13}}{-150}
$