7(3-x)=8(4-2x)x=-53/23

Solution for 7(3-x)=8(4-2x)x=-53/23 equation:

7(3-x)=8(4-2x)x=-53/23

We move all terms to the left:

7(3-x)-(8(4-2x)x)=0

We add all the numbers together, and all the variables

7(-1x+3)-(8(-2x+4)x)=0

We multiply parentheses

-7x-(8(-2x+4)x)+21=0


We calculate terms in parentheses: -(8(-2x+4)x), so:

8(-2x+4)x

We multiply parentheses

-16x^2+32x

Back to the equation:

-(-16x^2+32x)


We get rid of parentheses

16x^2-32x-7x+21=0

We add all the numbers together, and all the variables

16x^2-39x+21=0

a = 16; b = -39; c = +21;
Δ = b2-4ac
Δ = -392-4·16·21
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{177}}{2*16}=\frac{39-\sqrt{177}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{177}}{2*16}=\frac{39+\sqrt{177}}{32}
$