(10-3x)*(10-3x)=13

Solution for (10-3x)*(10-3x)=13 equation:

(10-3x)(10-3x)=13

We move all terms to the left:

(10-3x)(10-3x)-(13)=0

We add all the numbers together, and all the variables

(-3x+10)(-3x+10)-13=0

We multiply parentheses ..

(+9x^2-30x-30x+100)-13=0

We get rid of parentheses

9x^2-30x-30x+100-13=0

We add all the numbers together, and all the variables

9x^2-60x+87=0

a = 9; b = -60; c = +87;
Δ = b2-4ac
Δ = -602-4·9·87
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{13}}{2*9}=\frac{60-6\sqrt{13}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{13}}{2*9}=\frac{60+6\sqrt{13}}{18}
$