(x^2)/10=3x+22.5

Solution for (x^2)/10=3x+22.5 equation:

(x^2)/10=3x+22.5

We move all terms to the left:

(x^2)/10-(3x+22.5)=0

We get rid of parentheses

x^2/10-3x-22.5=0

We multiply all the terms by the denominator


x^2-3x*10-(22.5)*10=0

We add all the numbers together, and all the variables

x^2-3x*10-225=0

Wy multiply elements

x^2-30x-225=0

a = 1; b = -30; c = -225;
Δ = b2-4ac
Δ = -302-4·1·(-225)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30\sqrt{2}}{2*1}=\frac{30-30\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30\sqrt{2}}{2*1}=\frac{30+30\sqrt{2}}{2}
$