x^2=7-15x

Solution for x^2=7-15x equation:

x^2=7-15x

We move all terms to the left:

x^2-(7-15x)=0

We add all the numbers together, and all the variables

x^2-(-15x+7)=0

We get rid of parentheses

x^2+15x-7=0

a = 1; b = 15; c = -7;
Δ = b2-4ac
Δ = 152-4·1·(-7)
Δ = 253
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{-(15)-\sqrt{253}}{2*1}=\frac{-15-\sqrt{253}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{253}}{2*1}=\frac{-15+\sqrt{253}}{2}
$