-9/10*x+7=-24

Solution for -9/10*x+7=-24 equation:

-9/10*x+7=-24

We move all terms to the left:

-9/10*x+7-(-24)=0


Domain of the equation: 10*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-9/10*x+31=0

We multiply all the terms by the denominator


31*10*x-9=0

Wy multiply elements

310x*x-9=0

Wy multiply elements

310x^2-9=0

a = 310; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·310·(-9)
Δ = 11160
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:

$\sqrt{\Delta}=\sqrt{11160}=\sqrt{36*310}=\sqrt{36}*\sqrt{310}=6\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{310}}{2*310}=\frac{0-6\sqrt{310}}{620}
=-\frac{6\sqrt{310}}{620}
=-\frac{3\sqrt{310}}{310}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{310}}{2*310}=\frac{0+6\sqrt{310}}{620}
=\frac{6\sqrt{310}}{620}
=\frac{3\sqrt{310}}{310}
$