2x^2=11x-10

Solution for 2x^2=11x-10 equation:

2x^2=11x-10

We move all terms to the left:

2x^2-(11x-10)=0

We get rid of parentheses

2x^2-11x+10=0

a = 2; b = -11; c = +10;
Δ = b2-4ac
Δ = -112-4·2·10
Δ = 41
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{-(-11)-\sqrt{41}}{2*2}=\frac{11-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{41}}{2*2}=\frac{11+\sqrt{41}}{4}
$