10t(t+3)=7t-12

Solution for 10t(t+3)=7t-12 equation:

10t(t+3)=7t-12

We move all terms to the left:

10t(t+3)-(7t-12)=0

We multiply parentheses

10t^2+30t-(7t-12)=0

We get rid of parentheses

10t^2+30t-7t+12=0

We add all the numbers together, and all the variables

10t^2+23t+12=0

a = 10; b = 23; c = +12;
Δ = b2-4ac
Δ = 232-4·10·12
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-7}{2*10}=\frac{-30}{20}
=-1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+7}{2*10}=\frac{-16}{20}
=-4/5
$