x^2=15-3.5x

Solution for x^2=15-3.5x equation:

x^2=15-3.5x

We move all terms to the left:

x^2-(15-3.5x)=0

We add all the numbers together, and all the variables

x^2-(-3.5x+15)=0

We get rid of parentheses

x^2+3.5x-15=0

a = 1; b = 3.5; c = -15;
Δ = b2-4ac
Δ = 3.52-4·1·(-15)
Δ = 72.25
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{-(3.5)-\sqrt{72.25}}{2*1}=\frac{-3.5-\sqrt{72.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.5)+\sqrt{72.25}}{2*1}=\frac{-3.5+\sqrt{72.25}}{2}
$