x^2+5=2(5x-3)

Solution for x^2+5=2(5x-3) equation:

x^2+5=2(5x-3)

We move all terms to the left:

x^2+5-(2(5x-3))=0


We calculate terms in parentheses: -(2(5x-3)), so:

2(5x-3)

We multiply parentheses

10x-6

Back to the equation:

-(10x-6)


We get rid of parentheses

x^2-10x+6+5=0

We add all the numbers together, and all the variables

x^2-10x+11=0

a = 1; b = -10; c = +11;
Δ = b2-4ac
Δ = -102-4·1·11
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{14}}{2*1}=\frac{10-2\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{14}}{2*1}=\frac{10+2\sqrt{14}}{2}
$