3.50x2+4-3=11.50+3

Solution for 3.50x2+4-3=11.50+3 equation:

3.50x^2+4-3=11.50+3

We move all terms to the left:

3.50x^2+4-3-(11.50+3)=0

We add all the numbers together, and all the variables

3.50x^2+4-3-(14.5)=0

We add all the numbers together, and all the variables

3.50x^2-13.5=0

a = 3.50; b = 0; c = -13.5;
Δ = b2-4ac
Δ = 02-4·3.50·(-13.5)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{21}}{2*3.50}=\frac{0-3\sqrt{21}}{7}
=-\frac{3\sqrt{21}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{21}}{2*3.50}=\frac{0+3\sqrt{21}}{7}
=\frac{3\sqrt{21}}{7}
$