-5(3/4x-5)+7=1/2x+10

Solution for -5(3/4x-5)+7=1/2x+10 equation:

-5(3/4x-5)+7=1/2x+10

We move all terms to the left:

-5(3/4x-5)+7-(1/2x+10)=0


Domain of the equation: 4x-5)!=0

x∈R



Domain of the equation: 2x+10)!=0

x∈R


We multiply parentheses

-15x-(1/2x+10)+25+7=0

We get rid of parentheses

-15x-1/2x-10+25+7=0

We multiply all the terms by the denominator


-15x*2x-10*2x+25*2x+7*2x-1=0

Wy multiply elements

-30x^2-20x+50x+14x-1=0

We add all the numbers together, and all the variables

-30x^2+44x-1=0

a = -30; b = 44; c = -1;
Δ = b2-4ac
Δ = 442-4·(-30)·(-1)
Δ = 1816
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:

$\sqrt{\Delta}=\sqrt{1816}=\sqrt{4*454}=\sqrt{4}*\sqrt{454}=2\sqrt{454}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{454}}{2*-30}=\frac{-44-2\sqrt{454}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{454}}{2*-30}=\frac{-44+2\sqrt{454}}{-60}
$