3X2-3x=61.75

Solution for 3X2-3x=61.75 equation:

3X^2-3X=61.75

We move all terms to the left:

3X^2-3X-(61.75)=0

We add all the numbers together, and all the variables

3X^2-3X-61.75=0

a = 3; b = -3; c = -61.75;
Δ = b2-4ac
Δ = -32-4·3·(-61.75)
Δ = 750
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:

$\sqrt{\Delta}=\sqrt{750}=\sqrt{25*30}=\sqrt{25}*\sqrt{30}=5\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5\sqrt{30}}{2*3}=\frac{3-5\sqrt{30}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5\sqrt{30}}{2*3}=\frac{3+5\sqrt{30}}{6}
$