1/2(2x)=10x-21

Solution for 1/2(2x)=10x-21 equation:

1/2(2x)=10x-21

We move all terms to the left:

1/2(2x)-(10x-21)=0


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R


We get rid of parentheses

1/22x-10x+21=0

We multiply all the terms by the denominator


-10x*22x+21*22x+1=0

Wy multiply elements

-220x^2+462x+1=0

a = -220; b = 462; c = +1;
Δ = b2-4ac
Δ = 4622-4·(-220)·1
Δ = 214324
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:

$\sqrt{\Delta}=\sqrt{214324}=\sqrt{4*53581}=\sqrt{4}*\sqrt{53581}=2\sqrt{53581}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(462)-2\sqrt{53581}}{2*-220}=\frac{-462-2\sqrt{53581}}{-440}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(462)+2\sqrt{53581}}{2*-220}=\frac{-462+2\sqrt{53581}}{-440}
$