259=7(6x-3)2x

Solution for 259=7(6x-3)2x equation:

259=7(6x-3)2x

We move all terms to the left:

259-(7(6x-3)2x)=0


We calculate terms in parentheses: -(7(6x-3)2x), so:

7(6x-3)2x

We multiply parentheses

84x^2-42x

Back to the equation:

-(84x^2-42x)


We get rid of parentheses

-84x^2+42x+259=0

a = -84; b = 42; c = +259;
Δ = b2-4ac
Δ = 422-4·(-84)·259
Δ = 88788
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:

$\sqrt{\Delta}=\sqrt{88788}=\sqrt{196*453}=\sqrt{196}*\sqrt{453}=14\sqrt{453}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-14\sqrt{453}}{2*-84}=\frac{-42-14\sqrt{453}}{-168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+14\sqrt{453}}{2*-84}=\frac{-42+14\sqrt{453}}{-168}
$