4(5x-3)=7(2x+3)6x

Solution for 4(5x-3)=7(2x+3)6x equation:

4(5x-3)=7(2x+3)6x

We move all terms to the left:

4(5x-3)-(7(2x+3)6x)=0

We multiply parentheses

20x-(7(2x+3)6x)-12=0


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

7(2x+3)6x

We multiply parentheses

84x^2+126x

Back to the equation:

-(84x^2+126x)


We get rid of parentheses

-84x^2+20x-126x-12=0

We add all the numbers together, and all the variables

-84x^2-106x-12=0

a = -84; b = -106; c = -12;
Δ = b2-4ac
Δ = -1062-4·(-84)·(-12)
Δ = 7204
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:

$\sqrt{\Delta}=\sqrt{7204}=\sqrt{4*1801}=\sqrt{4}*\sqrt{1801}=2\sqrt{1801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-2\sqrt{1801}}{2*-84}=\frac{106-2\sqrt{1801}}{-168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+2\sqrt{1801}}{2*-84}=\frac{106+2\sqrt{1801}}{-168}
$