2x^2=52-5x

Solution for 2x^2=52-5x equation:

2x^2=52-5x

We move all terms to the left:

2x^2-(52-5x)=0

We add all the numbers together, and all the variables

2x^2-(-5x+52)=0

We get rid of parentheses

2x^2+5x-52=0

a = 2; b = 5; c = -52;
Δ = b2-4ac
Δ = 52-4·2·(-52)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-21}{2*2}=\frac{-26}{4}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+21}{2*2}=\frac{16}{4}
=4
$