4x+10=2x^2+5x-8

Solution for 4x+10=2x^2+5x-8 equation:

4x+10=2x^2+5x-8

We move all terms to the left:

4x+10-(2x^2+5x-8)=0

We get rid of parentheses

-2x^2+4x-5x+8+10=0

We add all the numbers together, and all the variables

-2x^2-1x+18=0

a = -2; b = -1; c = +18;
Δ = b2-4ac
Δ = -12-4·(-2)·18
Δ = 145
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{-(-1)-\sqrt{145}}{2*-2}=\frac{1-\sqrt{145}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*-2}=\frac{1+\sqrt{145}}{-4}
$