X=-1.2x^2+315x-0.03x^2-2x^2+70x+500

Solution for X=-1.2x^2+315x-0.03x^2-2x^2+70x+500 equation:

X=-1.2X^2+315X-0.03X^2-2X^2+70X+500

We move all terms to the left:

X-(-1.2X^2+315X-0.03X^2-2X^2+70X+500)=0

We get rid of parentheses

1.2X^2+0.03X^2+2X^2-315X-70X+X-500=0

We add all the numbers together, and all the variables

3.23X^2-384X-500=0

a = 3.23; b = -384; c = -500;
Δ = b2-4ac
Δ = -3842-4·3.23·(-500)
Δ = 153916
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:

$\sqrt{\Delta}=\sqrt{153916}=\sqrt{4*38479}=\sqrt{4}*\sqrt{38479}=2\sqrt{38479}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-2\sqrt{38479}}{2*3.23}=\frac{384-2\sqrt{38479}}{6.46}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+2\sqrt{38479}}{2*3.23}=\frac{384+2\sqrt{38479}}{6.46}
$