4(-2x+7)+10=-2(x-3)/2

Solution for 4(-2x+7)+10=-2(x-3)/2 equation:

4(-2x+7)+10=-2(x-3)/2

We move all terms to the left:

4(-2x+7)+10-(-2(x-3)/2)=0

We multiply parentheses

-8x-(-2(x-3)/2)+28+10=0

We multiply all the terms by the denominator


-8x*2)-(-2(x-3)+28*2)+10*2)=0

We add all the numbers together, and all the variables

-8x*2)-(-2(x-3)=0

We multiply parentheses

-8x*2)-(-2x+6=0

Wy multiply elements

-16x^2-2x+6=0

a = -16; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-16)·6
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{97}}{2*-16}=\frac{2-2\sqrt{97}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{97}}{2*-16}=\frac{2+2\sqrt{97}}{-32}
$