0=3.5x^2+18x-13.5

Solution for 0=3.5x^2+18x-13.5 equation:

0=3.5x^2+18x-13.5

We move all terms to the left:

0-(3.5x^2+18x-13.5)=0

We add all the numbers together, and all the variables

-(3.5x^2+18x-13.5)=0

We get rid of parentheses

-3.5x^2-18x+13.5=0

a = -3.5; b = -18; c = +13.5;
Δ = b2-4ac
Δ = -182-4·(-3.5)·13.5
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-3\sqrt{57}}{2*-3.5}=\frac{18-3\sqrt{57}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+3\sqrt{57}}{2*-3.5}=\frac{18+3\sqrt{57}}{-7}
$