7x^2-4x-18=2x^2-13x+114.244

Solution for 7x^2-4x-18=2x^2-13x+114.244 equation:

7x^2-4x-18=2x^2-13x+114.244

We move all terms to the left:

7x^2-4x-18-(2x^2-13x+114.244)=0

We get rid of parentheses

7x^2-2x^2-4x+13x-114.244-18=0

We add all the numbers together, and all the variables

5x^2+9x-132.244=0

a = 5; b = 9; c = -132.244;
Δ = b2-4ac
Δ = 92-4·5·(-132.244)
Δ = 2725.88
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{-(9)-\sqrt{2725.88}}{2*5}=\frac{-9-\sqrt{2725.88}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{2725.88}}{2*5}=\frac{-9+\sqrt{2725.88}}{10}
$