4x-5=2x^2-5x-10

Solution for 4x-5=2x^2-5x-10 equation:

4x-5=2x^2-5x-10

We move all terms to the left:

4x-5-(2x^2-5x-10)=0

We get rid of parentheses

-2x^2+4x+5x+10-5=0

We add all the numbers together, and all the variables

-2x^2+9x+5=0

a = -2; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·(-2)·5
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*-2}=\frac{2}{-4}
=-1/2
$