2x^2=15-8x

Solution for 2x^2=15-8x equation:

2x^2=15-8x

We move all terms to the left:

2x^2-(15-8x)=0

We add all the numbers together, and all the variables

2x^2-(-8x+15)=0

We get rid of parentheses

2x^2+8x-15=0

a = 2; b = 8; c = -15;
Δ = b2-4ac
Δ = 82-4·2·(-15)
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{46}}{2*2}=\frac{-8-2\sqrt{46}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{46}}{2*2}=\frac{-8+2\sqrt{46}}{4}
$