-75x^2+4.8x-0.3=25x^2+10.02-10^2

Solution for -75x^2+4.8x-0.3=25x^2+10.02-10^2 equation:

-75x^2+4.8x-0.3=25x^2+10.02-10^2

We move all terms to the left:

-75x^2+4.8x-0.3-(25x^2+10.02-10^2)=0

We get rid of parentheses

-75x^2-25x^2+4.8x-10.02-0.3+10^2=0

We add all the numbers together, and all the variables

-100x^2+4.8x+89.68=0

a = -100; b = 4.8; c = +89.68;
Δ = b2-4ac
Δ = 4.82-4·(-100)·89.68
Δ = 35895.04
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{-(4.8)-\sqrt{35895.04}}{2*-100}=\frac{-4.8-\sqrt{35895.04}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.8)+\sqrt{35895.04}}{2*-100}=\frac{-4.8+\sqrt{35895.04}}{-200}
$